Please tell me where I am mistaking in the following problem

1/5 < 3/5 (1)

therefore 1 x 5 < 3 x 5

and 5 < 15

but 1/5 = -1/-5 (2)

therefore from 1 and 2

-1/-5 < 3/5

therefore -1 x 5 < 3 x -5

and -5 < -15

but we know that this is not the case.

So please tell me where have I mistaken.