Answer
47/52
Work Step by Step
There are $\binom{52}{5} = \frac{52!}{47!5!}$ ways to choose a 5 card poker deck. If we omit the possibility of drawing the ace of hearts, there are $\binom{51}{5} = \frac{51!}{46!5!}$ ways to do so. Hence the probability is
$$\frac{51!}{46!5!} \frac{47!5!}{52!} = 47/52$$
