My boys loved the Wallace Collection -- very impressive displays of armor and arms, and tons of other things, plus it is in a really neat building. And admission is free, which is unusual in London! They also have an atrium restaurant that serves a very nice afternoon tea.
The Tower of London is great. Unfortunately it is probably too late for you to secure tickets for the Ceremony of the Keys (the evening ritual where they close and lock the Tower), but you should see it in the daytime anyway. It will be very busy at spring break, so go right when it opens and head straight for the Crown Jewels – otherwise the line will be VERY long.
If you want to see Stonehenge, we absolutely loved the small-group tour offered by The English Bus, called “Stonehenge, Bath and A Secret Place.” But with only 5 days, this might be better left for a later trip.
Absolutely agree that you must see the Churchill War Rooms.
My boys also loved Westminster Abbey.
The London Eye is a nice thing to do on your first afternoon/evening.
If you enjoy theater, tickets for West End shows are much more affordable than Broadway. We saw Hamilton there and it was fabulous – better than the performance we saw at the Kennedy Center, and better acoustics.
If you are looking for something quirky and offbeat, go to Sir John Soane’s Museum. We all thoroughly enjoyed it. A cool house full of collections and oddities. This is also free, though it is probably worthwhile to pay for the guidebook at the beginning, so you know what you are looking at during your self-guided tour.