Final answer:
The number of five-digit numbers with at least two equal digits is 62,352.
Step-by-step explanation:
To determine the number of five-digit numbers that have at least two equal digits, we can use the principle of complement. First, let's calculate the total number of five-digit numbers, which is 9 x 10 x 10 x 10 x 10 = 90,000. Next, let's calculate the number of five-digit numbers with all digits distinct, which is 9 x 9 x 8 x 7 x 6 = 27,648.
Subtracting this from the total gives us the number of five-digit numbers with at least two equal digits, which is 90,000 - 27,648 = 62,352.