An alternative to the tour bus:
From Euston, walk to Euston Square Underground station. (It's signposted). Take a Circle Line train (eastbound) to Tower Hill. (It's only about 15 minutes on the Tube). Walk to Tower Millennium Pier, taking in the first site (The Tower of London) as you do so, and the second one (Tower Bridge) upon your arrival there. Take an RB1 river bus to the London Eye. (Fare £6.80 or £4.50 if you've got a Travelcard). Services roughly every 20 minutes. Journey time 26 minutes, timetable here:
http://thamesclippers.s3.amazonaws.com/doc/TC-Online-TT-A4-April-2014.pdf )
Main sites along the way:
3. HMS Belfast
4. London Monument
5. The dome of St Paul's Cathedral
6. The Millennium Bridge
7. Tate Modern
8. The Oxo Tower
9. Cleopatra's Needle
10. The Southbank Centre
11 The London Eye
(That's a basic list; there's actually a great deal more to see on that short journey)
Then walk, with the river on you right, the short distance to Westminster Bridge (12. County Hall)
Cross Westminster Bridge to:
13. The Houses of Parliament
and
14. Westminster Abbey
Walk up Whitehall, passing:
15. The Cenotaph
16. Downing Street
and
17 Horse Guards' Parade
That takes you to
18. Trafalgar Square
19. Nelson's Column
and
20 The National Gallery
From there it's a few minutes walk to
21. Covent Garden Piazza
where (as well as all the free street entertainment) you can find loads of places for a well-earned drink and/or meal.
Hopefully there will still be time to walk to
22. Somerset House
Then walk to either Embankment or Charing Cross Underground station to take the Northern Line back to Euston. (If you need to end up somewhere else after your 5 hours, just let me know and I'll adjust the route accordingly).