The original function is \( f(x) = 4^x - 5 \), and it is transformed to \( 4^{2x} - 5 \).
In the transformation from \( f(x) \) to \( 4^{2x} - 5 \), we've essentially changed the \( x \) in the function to \( 2x \), which indicates a horizontal transformation. For the base of exponential functions, if you replace \( x \) with \( kx \) (where \( k > 1 \)), it results in a horizontal compression by a factor of \( \frac{1}{k} \).
In this case, since \( k = 2 \), this represents a horizontal compression by a factor of \( \frac{1}{2} \).
Thus, the correct identification for \( k \) is \( 2 \), and the transformation indicates a compression.
So the answer is: 2; compression.