To solve the equation 24 + 5x = 7^5 ÷ 7^3, we can simplify the right side of the equation first.

7^5 ÷ 7^3 can be simplified using the rule of exponents, which states that when dividing two numbers with the same base, you subtract the exponents.

So, 7^5 ÷ 7^3 = 7^(5-3) = 7^2 = 49.

Now, the equation becomes 24 + 5x = 49.

To isolate the variable x, we can subtract 24 from both sides of the equation:

24 + 5x - 24 = 49 - 24

This simplifies to:

5x = 25

Finally, to solve for x, we divide both sides of the equation by 5:

5x/5 = 25/5

This gives us:

x = 5