To simplify the expression \( 7(x+5) + 2(x+3) \), we will distribute the constants into the brackets and then combine like terms.
First, distribute \( 7 \) and \( 2 \):
\[ 7(x+5) = 7x + 35 \]
\[ 2(x+3) = 2x + 6 \]
Now, combine these results:
\[ 7x + 35 + 2x + 6 \]
Now, combine the like terms (\( 7x \) and \( 2x \), as well as \( 35 \) and \( 6 \)):
\[ (7x + 2x) + (35 + 6) = 9x + 41 \]
So, the simplified expression is:
\[ \boxed{9x + 41} \]