What is the value of $\left(2^3+5^2\right)\left(5^2-2^3\right)$?

First, let's calculate the values of the individual terms:
$$2^3=8$$
$$5^2=25$$
Substitute these values into the given expression:
$$(8+25)(25-8)$$
$$33\times 17=561$$
Alternatively, using the identity $(a+b)(a-b)=a^2-b^2$ where $a=5^2$ and $b=2^3$:
$$(5^2{)}^2-(2^3{)}^2=25^2-8^2=625-64=561$$