#### Answer

$-\frac{29}{4}$

#### Work Step by Step

According to the order of operations, we simplify inside parentheses, then we simplify powers, then we multiply and divide, and finally, we add and subtract. When we do this, we find:
$2^{-1}-\frac{1}{3^{-2}}+5\left(\frac{1}{2^2}\right) = \frac{1}{2}-3^2+5\cdot\frac{1}{4} = -\frac{17}{2}+\frac{5}{4} = -\frac{34}{4} + \frac{5}{4} = -\frac{29}{4}$