Well I may invest in an additional one in the future. Can the power supply I'm using handle two?
Yes. I run 2 5750 with a 500W Psu from months 24/7.
But if I were you, I would spend a little more for a 750W psu which would allow you to run 3 or maybe even 4 58XX cards.
Case and HD are superfluous for a miner.