To find the cost of the fence for Mr. Rodriguez's garden, we need to evaluate the expression \( 7(l + 2w) \) with \( l = 5 \) yards and \( w = 2 \) yards.
First, substitute the values of \( l \) and \( w \) into the expression:
\[ l + 2w = 5 + 2(2) \]
Now calculate \( 2(2) \):
\[ 2(2) = 4 \]
So now we can compute \( l + 2w \):
\[ l + 2w = 5 + 4 = 9 \]
Next, we calculate \( 7(l + 2w) \):
\[ 7(l + 2w) = 7(9) = 63 \]
Thus, the cost for the fence materials is \( \boxed{63} \).