To simplify the expression 500 - {5x[409 - (2^3x3 - 21)^2] - 1724}, we need to follow the order of operations (PEMDAS/BODMAS).

First, let's simplify the innermost parentheses:
2^3x3 - 21 = 8x3 - 21 = 24 - 21 = 3

Now, we can simplify the expression inside the square brackets:
[409 - (2^3x3 - 21)^2] = [409 - 3^2] = [409 - 9] = 400

Next, we can simplify the expression inside the curly braces:
5x[409 - (2^3x3 - 21)^2] = 5x400 = 2000

Finally, we can simplify the entire expression:
500 - {5x[409 - (2^3x3 - 21)^2] - 1724} = 500 - (2000 - 1724) = 500 - 276 = 224