Given that \( h^{-1}(5) = -2 \), this means that if you input \( 5 \) into the inverse function \( h^{-1} \), you get \( -2 \). By the definition of an inverse function, this tells us that applying the function \( h \) to \( -2 \) gives us \( 5 \).
In mathematical terms, this is expressed as:
\[ h(-2) = 5 \]
Thus, the answer is:
\[ h(-2) = 5 \]