Apart from what is already being worked on. like Crossrail, Thameslink 2000 and the Northern Line bifurcation to Battersea (grrgh!) nothing of any significance is going to be happening with rail in the Greater London area in the next five years at least, which is why Sir Peter Hendy was warning a few months ago of the potential for civil disorder with a rapidly increasing population desperate to travel to and from work and being frustrated. The only answer a cash-strapped TfL has been able to come up with was an extra 500 buses over that five year period, although even that remains unfunded. In any case, traffic congestion in Outer London and parts of Inner London, combined with more notional 20 mph speed limits and speed humps, is leading to more buses being put on to the road every month just to maintain frequencies: an extra bus on each route would alone take up almost all those extra 500 buses without any palpable difference being seen by the passenger. Lover of buses I may be, but I also recognise they cannot solve all London's coming transport problems, or even a significant part of them.
With Gatwick very likely to be given the go-ahead for a second runway, my thoughts are of a new RER type service from there via East Croydon and a limited number of other stops to Victoria, then via Hyde Park Corner, Marble Arch, Paddington, Cricklewood, Brent Cross to ? Perhaps Thameslink 2100, to be completed by 2200. Gatwick to Heathrow would also be feasible this way.
"In the next five years" is rather an odd statement to make, given that if anything were to start in the next five years, it wouldn't be completed until well after that. Things could certainly get kicked off in the next five years, but these things have to go through consultation. Things such as:
Crossrail 2
Bakerloo extension
HS2
Crossrail extension to WCML Outers
Old Oak Common Station
New Tube for London (and associated line upgrades)
SWML 5th Track
Given that the projects you've mentioned
Crossrail
Thameslink Programme
Battersea Extension
Will all be completed in the next 5 years, alongside
Barking Riverside extension of GOBLIN
GOBLIN electrification
SSL Upgrade
Camden Town Upgrade
Extra platforms at East Croydon
These will all perform various changes which greatly improve capacity into and around London. Don't underestimate the impact of some of these. SSL Upgrade will allow a far greater frequency along the entire Subsurface railway. Lots and lots more S7s moving people around the Circle, District, H&C and Metropolitan lines. GOBLIN electrification will allow 2 car DMUs to be upgraded to 4 car EMUs (with frequency improvement?). The extra platforms at East Croydon will also allow more trains to pass through (and stop at) the station without huge capacity constraints.