I very much recommend you read
this essay on the Master's sexuality. And then
this one.
My take on Time Lords and sex is a bit different.
It's not very important, but it does exist, and is one way to procreate, if not the most popular. (Yes, I will gladly take Looms without that stupid fertility curse attached.)
It is, like most things on Gallifrey, a ceremonial event. It's about connecting on a mental level as well and physical. It's a rare expression of private intimacy, of veiled sensuality, of life itself. There are, of course, different rituals for different kinds of sex, different emotions and motivations.
It's tedious, is the thing. There's nothing spontaneous about it.
If the Doctor ever did have sex on Gallifrey, he certainly didn't do it the proper way. It was in part to flaunt the conventions, to be his own person; it being fun was just a bonus.
So Gallifreyans do have sex drives, and they do on occasion indulge them. They are not as powerful as a human's, and are more easily controlled. (Because they don't have to be, and Gallifreyans have more control over their bodies.)
This makes it a bit easier for the Doctor not to indulge in it, and by and large, I don't think he does. (There's a reason that, for 'sexuality', I often put 'flexible, often ignored'.)
For one thing, it just isn't a priority. He has other things to do - wonders to see, worlds to save, people to change.
For another, the people he's with most often are companions, and he knows it will usually complicate things, and he doesn't want to deal with that. (See
this prompt for my take on it, if you'd like.)
So he's not usually thinking about it, and when he does, he often tries to stop.
When it comes to the Fifth Doctor, I tend to think he never had sex in canon, though he fell for certain people. I think he may be the least likely to, because he is, in short, a repressed martyr with a guilt complex.
This Doctor doesn't deal well with intimacy; he doesn't even embrace his friends very often. There's nothing wrong with sex, provided it's consensual, but he'd rather not hear about it, thank you.
If someone makes sexual advances, he will probably be flustered and confused; he doesn't expect people to be attracted to him. Sometimes he'll try to talk it out; sometimes he'll pretend to be oblivious; sometimes he really will be.
I don't think this means he could never get to that point - obviously, as I've written it a number of times.
Let's take a look, shall we?
Open Verse
Sarah Jane
Sarah was and is very good at tearing down his many barriers. Part of this is because he knew her as Four, who wasn't so closed and insecure. Part of this is because she is, quite simply, Sarah Jane.
She made certain he knew that yes, she wants this, no, she won't regret it, and would you please stop treating me like a child before I hit you on the head.
She was confident and direct, understanding and compassionate, a reminder of an easier life, a dear friend.
Nyssa
Five fell slowly but surely in love with Nyssa. He never said anything, and neither did she, because they're both careful and proper and reserved.
When they met again, they were both older, she more confident and he more open; slowly but surely, they grew comfortable with their own emotions, and eventually they became intimate.
His interest in Nyssa was always more…cerebral, emotional, than sexual, but he always thought her beautiful, and he cherished the intimacy they shared.
Turlough
Turlough insisted on wearing a tight schoolboy's uniform, how fair is that?
Ahem. The Doctor connected with Turlough, as a fellow exile, a stranger in a strange world, a bright, antagonistic rebel. It was easy to forgive him, to guide him towards something better, to be his friend.
As for something else, well, beyond lingering glances and a lack of personal space, he never acted on his attraction.
Then Turlough returned to him as well, and they went a bit further, because the rules had changed, and he was tired of resisting everything around him.
The Poet and the Muse
Aislinn
The Doctor didn’t want to fall for her, as at the time she was involved with his future self. He did anyway, despite himself, because she's brave and beautiful and vulnerable, trying to find herself just as he did as a young man, struggling with a difficult, confusing world.
He wanted to show her that she, herself, was amazing, that she could be loved completely with no strings attached, that he would care for her no matter her nature, no matter what was in her past.
Eventually, in one universe, she chose him. Aislinn is a very sensual, tactile person; she had him embracing her even as they became friends, and it was easy for him to move forward.
Byron
He didn't plan on falling for Byron, either; it took him quite by surprise. It shouldn't have, really; he admired the poet before ever meeting him, and when he did, the man was captivating.
Far from perfect, of course, and the Doctor let him know it - but also that he was extraordinary, that potential never fades, that he's more than his legend.
One day, the Doctor sealed it with a kiss - awkward, tentative, but passionate. Eventually, he would become comfortable in his own sexuality.
Aislinn and Byron, of course, already had a complicated relationship; the Doctor wanted them both to feel equal, cherished, loved. By him, and by each other. It will never be perfect, because nothing is perfect, but that's all right.
It felt only natural to accept a proposal.
Oncoming Storms
Ushas
The Rani, of course, was very different from the girl he knew at Academy, but the Doctor didn't care; he refused to let another friend slip through his grasp, become an enemy instead. He had burned Koschei alive - he wouldn't deny Ushas.
She was just as brilliant as before, just as daring, and he enjoyed their banter as much as ever. They understood each other in ways no one else did, even if they failed to in others.
They were both strong and vulnerable in turns, and began to lean on each other, breaking their own rules.
Certainly he could have broken that one, as well.
Paradisa
Lucy
This is, by and large, not a sexual relationship; she is his companion, and he does not have sex with companions.
However, during a loss that banished his restraint, his suppression, the control that kept him sane, she kissed him, and he let her. Their clothes never came off, but pleasure was certainly had.
He blames himself for letting it happen, because it did in fact complicate things. Lucy is certainly beautiful, desirable, but she was always a friend first and foremost, and he wanted it to stay that way. He had no experience with romantic relationships, and he didn't want to her hurt her. Since then, he's tried his best to keep it platonic.
Later that night, of course...
The Master
The Master has always been a point of contradiction for the Doctor. They started out as best friends, and never entirely lose that, even once Four regenerates. Five never could, after all, bring himself to directly kill the man until Planet of Fire, and seemed to enjoy bantering with him. (Susan, in The Five Doctors, mentioned that they looked like friends. Well, up until the Doctor nicked the Master's recall device and left him to the Cybermen. Moving on.)
It was, in part, that murder that spurred on his relationship with the Master in Paradisa.. The guilt ate at him until he died; the Master's voice was the last he heard before regenerating.
The Doctor felt responsible for him, as his friend and enemy and killer.
Both had died horribly; both needed something to ground them. Something distracting, something powerful, something familiar.
Slowly, the Master began to heal, and the Doctor began to accept living instead of dying.
Of course, when the Doctor lost his inhibitions, the Master was going to take advantage, to manipulate the situation in his favour.
He made the Doctor furious, made the Doctor passionate, and then turned that passion to something else. (In part, perhaps, so he wouldn't get backhanded again.)
Since then, they've been in a...not quite romantic relationship. They do love each other, but they also hate each other, and hurt each other, and use each other. Sex is just one more part of that, an expression of and an opening for it.
So, in short? The Doctor isn't usually interested, but he certainly can be, given the right person and the right time.
Warning: it got long. 1,463 words long.