You shouldn't even have to ask. Your system is weak. Weak CPU, not enough RAM, weak video card.
Your CPU qualifies for the minimum requirement, but you need at least 1GB RAM & a Geforce 6600 or better.

The recommended specs are an Intel Core 2 Duo CPU, 2GB RAM & a Geforce 7900GT or better.

If you wanna play Bioshock & play it reasonably well, you're gonna have to drop at least $150 into your system.

WoW! Your running Bioshock on a 5200!!!!?!? Sweet? Can you make a recording in Fraps please? I would love to see how it performs!
I would also love to see how a 5200 Ultra would stack up in Bioshock.

Anyways, You running an 865 chipset, so either socket 478, or 775, wont support core CPUs. Upgrade to something like this:

P4 HT 2.8(higher is better)
1gb PC3200 RAM(or more)
Geforce 6800GT(or maybe a 7600 512mb both are under $80, the 6800GT is $68 right now!)

You will at least be able to play the game then at a reasonable Frame rate and spend under $200.00 for all the new gear.

Core2 Duo 1.86
1GB DDR2 667
Nvidia 8500GT
Asus P5L-MX