To solve this logarithmic expression, we need to use the properties of logarithms.

First, let's rewrite the expression as:

log_0.5(4) + log_5(√25)

Now, let's simplify each logarithm separately.

Using the change of base formula for the first logarithm:
log_0.5(4) = log(4) / log(0.5)
log_0.5(4) = log(4) / log(1/2)
log_0.5(4) = log(4) / (-log(2))
log_0.5(4) = log(4) / (-0.3010)
log_0.5(4) ≈ -3.3219

Now, simplify the second logarithm:
log_5(√25) = log(√25) / log(5)
log_5(√25) = log(5^(1/2)) / log(5)
log_5(√25) = (1/2)log(5) / log(5)
log_5(√25) = 1/2

Now, add the simplified logarithms back together:
-3.3219 + 1/2
= -3.3219 + 0.5
≈ -2.8219

Therefore, log_0.5(4) + log_5(√25) is approximately equal to -2.8219.