Let's simplify the expression step by step:
Start with the original expression:
\[ 5(3x + 2y) + 2x + 7y \]
Distribute the 5:
\[ 5 \cdot 3x + 5 \cdot 2y + 2x + 7y \] \[ 15x + 10y + 2x + 7y \]
Combine like terms:
For \(x\) terms:
\[ 15x + 2x = 17x \]
For \(y\) terms:
\[ 10y + 7y = 17y \]
Putting it all together:
\[ 17x + 17y \]
This result matches with the expression \(17x + 17y\), so the correct simplified expression is:
\[ 17x + 17y \]