It really depends on the PSU. Open the side of the case and look at the PSU. There should be a chart with the brand/model. Tell us that as well as the listed amperage on the +12v rail(s).
That said if you are willing to spend around $200 you can afford both a GTX 460 768mb and a new PSU;http://www.newegg.com/Product/ComboDealDetails.aspx?ItemList=Combo.567276
That's a lil over before rebate and under after. They average $200 anyway. The PSU is overkill really but it is one of the best brands you can buy and should cover SLI if you ever want to add a second card. The GTX 460 768mb is much faster than the HD5770 and can also overclock a very large amount. The DirectCU card in particular has very effective and quiet cooling.