5 days is a little on the short side, but I think you can see most of what you want to see, or at the very least all the important stuff, in that period of time. DW and I went 2 years ago for our 25th anniversary, in one long trip that included a week in Hawaii to get DD settled in at university, and 4 days of meetings for megacorp in Germany on the backside of our visit to London. We stayed in London for 5 full days and at the end, we had gone completely thru our list of things we had wanted to see. Honestly, by that time we were exhausted, because we walked to and from most of the venues, between venues, and back to the hotel most days, with a bus ride here and there. This was in September, and for then entire 5 days we were there we had mostly sunny conditions with a few clouds here and there. It rained as we were at the airport leaving for Germany. It was cool in the mornings, but since we did a lot of walking, we kept warm enough in either short sleeves for me, and briefly here and there a very light sweater for DW. I would say go prepared for worse weather than that, but that's how the weather treated us.
The attractions noted above cover most of what we visited. I advise that you get a travel guide, read thru it and decide which attractions are of most interest long before you go so you can plan the "must see" list, and also perhaps a day or two of spontaneous wandering.
Good luck and have fun!
R
Heck, I used to walk across the bridges all the time... so it being long was not a problem...
