Short Answer 
A total of 30 valid numbers greater than 500 can be formed using the digits 2, 3, 4, and 5 without repetition. This includes 6 valid 3-digit numbers starting with 5 and 24 permutations for 4-digit numbers.
Step 1: Identify the Digits and Conditions
We have four digits available: 2, 3, 4, and 5. Our goal is to form numbers that are greater than 500 by ensuring that no digits repeat in any number. This means we need to focus on the valid number lengths and how to structure them to meet our conditions.
Step 2: Determine Valid Number Lengths
Since we are looking for numbers greater than 500, it is essential that the numbers have at least 3 digits. Specifically, the first digit must be 5 in any 3-digit format, as any other starting digit would yield a number less than 500. This leads us to focus on forming both 3-digit and 4-digit numbers using the available digits.
Step 3: Formulate and Sum the Valid Numbers
First, by using 5 as the first digit, we can create 6 valid 3-digit combinations: 523, 524, 532, 534, 542, and 543. Next, we can form 4-digit numbers using all permutations of the digits, resulting in 24 valid combinations. Adding these gives us a total of 30 valid numbers greater than 500.