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.