It may well work for you with your current power supply. On my own PC I upgraded to the recommended 750w for my card, and on a few other PC's I have built I have always gone for the recommended.
The card dimensions are 144x69x33mm so measure your case to see if you have enough clearance for this card. The recommended power is 400w. In my experience having the recommended power supply is always the best way to go.
Also does your motherboard support PCI-E 3.0 x16? or can you post what motherboard you are using?
It may well work for you with your current power supply. On my own PC I upgraded to the recommended 750w for my card, and on a few other PC's I have built I have always gone for the recommended.