3 thinsg mainly:
-depending on if your current slot for the Video Card is AGP (should be compatible as far as AGP speeds go if its running a Geforce 5500).
-If You can get an AGP version of the HD3850.
-Your Powersupply is powerful enough to run the card, has enough wattage & amps on 12V line.
then yes, it should be able to support it.
the first 2 are more specifically related to the Motherboard. if you can get an AGP HD3850, & the Motherboard has an 8x AGP slot should be good to go, just need to make sure the PSU can handle it... also make sure you have enough room in the case for the card, as the 3850 is a fair bit longer than the old Geforce FX5500's were.
heat output is also much more, make sure you have efficient intake & exhaust setup for cooling.
the other thing is, I'm not sure, but your current CPU could be holding back the 3850's potential performance too, but in any case, if a bottleneck could happen, the performance you'd get up to the Bottleneck would be greater than the old card anyways, so might still be worth it, depending on how much you'd pay for the card.
for the Motherboard, check on the board, there should be some print somewhere stating the Model number or designation of the board, other than a serial number.
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