To simplify the expression \( 5h + 8h + 6h^2 + 10 \), we can combine like terms.
The terms with \( h \) are \( 5h \) and \( 8h \):
\[ 5h + 8h = 13h \]
Now, we can rewrite the expression with the combined terms:
\[ 13h + 6h^2 + 10 \]
Since \( 6h^2 \) and \( 10 \) are not like terms with \( h \), we can only combine the \( h \) terms.
Therefore, the simplified expression is:
\[ 6h^2 + 13h + 10 \]