Have a browse of the Nokia store for games that are compatible for the C5-03 and see what takes your fancy or not.
All the best.
can nokia c6-01 games work on the c5-03
The C6-01 is based on a newer version of Symbian than the C5-03, so there is no guarantee that Symbian/Qt based games made for the newer OS will run on an older OS version. But it pretty much depends on the game (how it was written, which SDK - Software Development Kit - the developer actually used,e tc.).
It also depends on whether the developer has explicitely ruled out installation on some specific version of the OS or not, or if distributing through the Nokia/Ovi Store, if they've restricted availability/compatibility there.
Note that for Java or Flash Lite based games/apps, there should not be any significant difference.