To evaluate the expression \(11r^2 - 5\) for \(r = 2\), follow these steps:
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Substitute \(r = 2\) into the expression: \[ 11(2)^2 - 5 \]
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Calculate \(2^2\): \[ 2^2 = 4 \]
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Substitute this back into the expression: \[ 11(4) - 5 \]
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Multiply \(11\) by \(4\): \[ 44 - 5 \]
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Finally, subtract \(5\) from \(44\): \[ 44 - 5 = 39 \]
Thus, the value of the expression for \(r = 2\) is \(\boxed{39}\).