Verified answer

You should rewrite problem as an exponent

5^-4=2x-5

simplify

.0016=2x-5

add 5 to each side

5.0016=2x

x=2.5008

2x - 5 = 5^-4

2x = 5.0016

x = 2.5008

if it as ---------

log_5 (2x-5) = -4

so 2x- 5 = 5^-4

2x = 1/5^4 + 5

2x = 1/625+5

x =3126/1250

= 2.5008 answer