$\\frac{5}{2^3 + 1} + 4 - 2^2$

$\frac{5}{2^3 + 1} + 4 - 2^2$

First, calculate the exponents in the expression. We know that $2^3 = 8$ and $2^2 = 4$. So the expression becomes $\frac{5}{8 + 1}+4 - 4$.

Simplify the denominator of the fraction: $8 + 1 = 9$, so now we have $\frac{5}{9}+4 - 4$.

Notice that $4 - 4 = 0$, so the expression simplifies to $\frac{5}{9}+0$.

$\frac{5}{9}$