You need to qualify as a pattern day trader, which means you must have $25k in equity/cash minimum in an account. So in your example no you couldn't. But if you have $50k cash in your account, yes you could buy $10k worth of stock using only $5k cash.
FYI ironchef if you have less than $25k in your account you can only buy and sell a position during the same day 3 times per week max.
http://en.wikipedia.org/wiki/Pattern_day_trader
This doesn't apply to FOREX btw.