In order to belong to the interval (-5, 13), you have to be (strictly) greater than -5 and (strictly) less than 13.
So, we want
[tex]-5<5y-7<13[/tex]
We can add 7 to all sides:
[tex]-5+7<5y-7+7<13+7 \iff 2<5y<20[/tex]
And divide all sides by 5:
[tex]\dfrac{2}{5}<y<4[/tex]
