To find the cost of the fence for Mr. Rodriguez's garden, we first need to evaluate the expression \( 7(l + 2w) \) using the given dimensions.
Given:
- Length \( l = 5 \) yards
- Width \( w = 2 \) yards
Now, substitute the values into the expression:
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Calculate \( 2w \): \[ 2w = 2 \times 2 = 4 \]
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Now substitute \( l \) and \( 2w \) into the expression \( l + 2w \): \[ l + 2w = 5 + 4 = 9 \]
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Multiply this sum by 7 to find the total cost: \[ 7(l + 2w) = 7 \times 9 = 63 \]
Thus, the cost for the fence is \( \boxed{63} \).