To find the value of the function \( f(x) = -3x^2 + 5 \) at \( x = -2 \), we substitute \(-2\) into the function:
\[ f(-2) = -3(-2)^2 + 5 \]
Calculating \((-2)^2\):
\[ (-2)^2 = 4 \]
Now substitute that back into the equation:
\[ f(-2) = -3(4) + 5 \]
Calculating \(-3(4)\):
\[ -3(4) = -12 \]
So we have:
\[ f(-2) = -12 + 5 \]
Finally, calculating \(-12 + 5\):
\[ f(-2) = -7 \]
Thus, the value of \( f(-2) \) is \(-7\).