To find the cost for the materials needed to build the fence around Mr. Rodriguez's garden, we can use the formula given:
\[ \text{Cost} = 7(l + 2w) \]
where \( l \) is the length and \( w \) is the width of the garden.
We know that:
- \( l = 5 \) yards
- \( w = 2 \) yards
First, we calculate \( l + 2w \):
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Calculate \( 2w \): \[ 2w = 2 \times 2 = 4 \]
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Now calculate \( l + 2w \): \[ l + 2w = 5 + 4 = 9 \]
Now we can find the total cost:
\[ \text{Cost} = 7(l + 2w) = 7 \times 9 = 63 \]
So, the cost for the fence is \( \mathbf{63} \).
The answer is:
$63