what are some graphics cards compatable with my asus A55BM-E motherboard

Your Motherboard has a PCI-E x16 3.0 Graphics Card port. That's a good sign. It means it's compatible with all cards currently on the market and will continue to be for at least a few years to come.

However, the rest of the specifications of your computer will limit what Graphics Cards you can consider. Most importantly is the Wattage of your PSU (Power Supply Unit).

RAM and CPU are also important factors.

Post your full rig specs and we can give you a good idea of what cards you can consider.
 
my full system spcs are
CPU: Duel AMD A6-5400K APU 3.7ghz (stable overclocked at 4.4 ghz)
GPU AMD Radeon 7540 HD graphics with 760 mhz speed
120 GB HDD
350 watt Power supply I think
4GB Duel Channel RAM at 1333 MHZ speed
 
With a 350w PSU your options are quite limited when it comes to Graphics Cards.

If you can confirm your PSU wattage or post the manufacturer and model of the PSU (should be evident on a sticker on the back of the PSU) we can get a clear idea of what Graphics Cards will run safely in that rig.

How long ago did you purchase this machine and was it self-assembled or an all-in-one purchase?