Rounds For A Monte Carlo Estimate

A deck holds 63 cards numbered 1 to 63. You draw the top 5 cards, and you win the round when the five numbers come out in strictly ascending order.

Instead of trusting your algebra you plan a Monte Carlo run: simulate $N$ independent rounds and report the observed win fraction $\hat{p}$. You want the standard error of $\hat{p}$ to be at most 0.0005.

What is the smallest $N$ that achieves that? Use the exact win probability as $p$ in the standard error.

Answer format: enter an integer.