To simplify the expression \( -5 + 34(8h + 12) - 10h \), we start by distributing the 34:
\[ 34(8h + 12) = 34 \cdot 8h + 34 \cdot 12 = 272h + 408 \]
Now, we can rewrite the original expression by substituting what we found:
\[ -5 + 272h + 408 - 10h \]
Next, we combine the like terms. Start with the \(h\) terms:
\[ 272h - 10h = 262h \]
Now, combine the constant terms:
\[ -5 + 408 = 403 \]
Putting it all together, we have:
\[ 262h + 403 \]
Thus, the simplified expression is:
\[ \boxed{262h + 403} \]
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