Yep.
The HD 5770 is nearly as powerful as the older HD 4870; I'm talking about less than a 5% performance difference. The HD 5770 consumes around 63w off the top of my head and the HD 4870 is about 120w.
That's 57w savings per hour. Suppose you game 30 hours a week for a year. That works out to a difference 82.7KWH in 52 weeks. The national average per KWH is roughly $0.12, that works out to roughly $9.92 difference per year. If you live in a city where it's about $0.22 per KWH, then that's $18.19 difference per year. If you live in a rural area where it's $0.07 per KWH, then that's only $5.79 difference per year.