First, simplify the expression:

log₁₀ 250 = log₁₀ (10*25) = log₁₀ 10 + log₁₀ 25 = 1 + 2 = 3

log₁₀ 2 = log₁₀ 2 = 0.3010

Therefore, log₁₀ 250 - log₁₀ 2 = 3 - 0.3010 = 2.6990

log₁₆ 36 = log₁₆ (6*6) = log₁₆ 6 + log₁₆ 6 = 1 + 1 = 2

log₁₀ 5 + log₁₆ log₆ 36 = log₁₀ 5 + log₁₀ 2/log₁₀ 16 = log₁₀ 5 + log₁₀ 2/4 = log₁₀ 5 + 0.5

Now, substitute the values:

2.6990 + log₁₀ 5 + 0.5 = 2.1990 + log₁₀ 5

Therefore, the final simplified expression is 2.1990 + log₁₀ 5.