The game requires a DX9 compatible card, but it doesn't require a card with DX9 features (like Pixel Shader 2.0). So the following cards would be able to run the game: GF 3, GF 4 Ti (not MX!), Radeon 8500, Radeon 9000 and above, Geforce FX, 6, 7, and the Radeon X-series.
If you want to get a card at a reasonable price, the FX5500 might be a bad idea performance-wise. It's a better choice than a Geforce 3, but inferior to the GeForce Ti 4200/4400/4600/4800 cards. Although the Ti 4x00 series cards dont't boast DX9 features, their performence is better than that of an FX5500.
An FX 5500/5600 card is too weak to give an enjoyable gaming experience in a DX9-heavy game, anyway.
What's your budget?
Depending on your budget, there could be lots of better alternatives than the ones I've mentioned above.
Also, here's a
link to the Matrix online FAQ.