To evaluate the expression \( 2a^2 + c^3 \) given the values \( a = 3 \), \( b = 4 \), and \( c = 5 \), we can substitute the values of \( a \) and \( c \) into the expression.
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First, calculate \( a^2 \): \[ a^2 = 3^2 = 9 \]
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Next, calculate \( c^3 \): \[ c^3 = 5^3 = 125 \]
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Now substitute these values into the expression \( 2a^2 + c^3 \): \[ 2a^2 + c^3 = 2(9) + 125 \]
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Calculate \( 2(9) \): \[ 2(9) = 18 \]
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Finally, add \( 18 \) and \( 125 \): \[ 18 + 125 = 143 \]
Thus, the value of the expression \( 2a^2 + c^3 \) when \( a = 3 \), \( b = 4 \), and \( c = 5 \) is \( \boxed{143} \).