The 5770 is a very weak card and only requires 50Watts or 4 amps more than the 220. I would think your PSU should be able to handle another 50W load unless you're already pushing it.
Another thing to consider is the fact you have an HP, which like most OEMs, have special parts which may or may not be compatible with aftermarket components. I would highly doubt you can just pop any standard PSU in the computer.
I wouldn't buy a PSU until you try using the 5770 on your existing system.