The given expression is: \[ (3h^{2} + 7h + 5) - (3h^{2} + h + 5) \]
First, distribute the negative sign to the terms inside the second parentheses: \[ 3h^{2} + 7h + 5 - 3h^{2} - h - 5 \]
Combine the terms with the same degree of \( h \):
So, the expression simplifies to: \[ 6h \]
\[ \boxed{6h} \]
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