(log5 (2)- log 5(4))/log5 (16)-log 5 (0.5))

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To solve this expression, we first simplify the logarithms using the properties of logarithms:

(log5 (2) - log5 (4)) / (log5 (16) - log5 (0.5)
= log5 (2/4) / log5 (16/0.5
= log5 (1/2) / log5 (32)

Next, we can simplify further by rewriting the numerator and denominator using the change of base formula:

= log(1/2) / log(32
= log(1/2) / log(2^5
= log(1/2) / 5log(2
= -log(2) / 5log(2
= -1 / 5

Therefore, the final result is -1/5.