How many 5 digit numbers have the product 6!?

To find how many 5-digit numbers have a product of digits equal to (6!) (which is 720), we first need to factor 720 into its prime factors: (720 = 2^4 \times 3^2 \times 5). A 5-digit number can consist of digits from 0 to 9, but since it cannot start with 0, we must consider valid combinations of the digits that meet the product requirement while ensuring one of the digits is non-zero. The specific combinations need to be calculated, but generally, the problem requires enumeration of valid digit groups, which can be complex and may require computational assistance for a precise count.