Two cards are drawn from a standard 52-card deck without placing the first card back into the deck before drawing the second one. Find the probability of drawing a queen $(Q)$ and then drawing a 5.

Step 1 ：Step 1: Understand the problem

Step 2 ：Step 2: Calculate the probability

Step 3 ：Step 3: Simplify the result

Step 4 ：Step 4: Check the result

Step 5 ：The probability of drawing a queen and then drawing a 5 is \(\boxed{\frac{4}{663}}\)