Lemon Balm. I don't find it invasive; what it is, is vigorous. It'll grow 2-3 feet tall and make a nice bush in the herbacious border like other perennials. But again like perennials, it doesn't really get much bigger, although you can lift-and-split successfully.
Supermarket herbs: Thyme grows brilliantly. I bought 4 pots from Asda for 49p each and split them into 10+ plants each. Within four weeks, 30' of slightly ugly brickwork along the edge of some beds was covered. Chives and parsley and mint and corriander and basil - just tip the pot out into the ground as is and it'll grow nicely for you.
Lemon balm goes very nicely in Pimms. It also smells nice in the border. Apart from that... it's super as a decoration for puddings - e.g. lemon meringue pie (which I hate), put a few leaves on the top.
Beware the curry plant. It smells like curry and garden centres will recommend that you cook with it. Dr Hessyan (sp?) tells us that it is toxic.
I don't see the point in restricting myself to five herbs... they're outside the back door, at the entrance to the garden and can be picked without stepping outside. Useful living in our current monsoon climate!
Rosemary, Sage (fry the leaves briefly and serve with calves liver, mmmmm), Thyme, Parsley, Oregano.