-1<-1/5x

I do not know if you mean

-1 < -(1/5) x
or
-1 < -1/(5x)

I will assume the first.
1 > (1/5)x
reverse arrow when multiplying by negative quantity
5 > x
or
x < 5
============
always check
if x = 0
is
-1 < -(1/5) 0
?????
yes -1 < 0