I had a very fussy colleague train me in making him tea in a mug. It takes nowhere near 5 minutes.
- Put the teabag in the mug while the kettle is boiling
- Use the hottest water you can; it should go into the mug immediately after boiling
- Fill the mug almost to the brim; when you remove the teabag it will make room for milk
- It doesn't take long to get the best of the flavour out. 20 seconds or so; long enough to get the milk from the fridge and find a teaspoon.
- Fish the bag out with a teaspoon; maybe give it a squeeze against the inside wall of the mug
- add sugar (if wanted) then milk (if wanted)
With this method, the tea is still piping hot when it's ready.
If you prefer tea that's been steeped for ages, of course I won't stop you :). Please don't do it if you're making tea for me though!
You would steep for longer in a teapot, but that's because one normal teabag is enough for at least two mugs of tea -- unless you've bought special one-cup teabags, such as you get in hotel rooms.
This applies to ordinary tea and Earl Grey -- things could be different for fruit teas and green tea.