Let's evaluate the expression:

\[
\log_2^4 + \log_4^2 - \log_{25}^5
\]

We'll break it down step by step.

1. Simplify \(\log_2^4\):
Since \(\log_2^4\) represents \((\log_2 4)\), and we know:
\[
\log_2 4 = \log_2 (2^2) = 2
\]

2. Simplify \(\log_4^2\):
\[
\log_4^2 = (\log_4 2)
\]
Use the change of base formula:
\[
\log_4 2 = \frac{\log_2 2}{\log_2 4}
\]
Given \(\log_2 2 = 1\) and \(\log_2 4 = 2\):
\[
\log_4 2 = \frac{1}{2}
\]

3. Simplify \(\log_{25}^5\):
\[
\log_{25}^5 = (\log_{25} 5)
\]
Rewrite 25 as \(5^2\):
\[
\log_{25} 5 = \frac{\log_5 5}{\log_5 25} = \frac{1}{2}
\]

4. Combine the results:
\[
\log_2^4 + \log_4^2 - \log_{25}^5 = 2 + \frac{1}{2} - \frac{1}{2}
\]
\[
= 2 + 0 = 2
\]

So, the value of the expression is:

D. 2