I would recommend getting x alone in the second equation so that you can substitute whatever x equals to in the first equation. This is what I'll be doing for my first step:
x=-5y-19
Then, substitution:
3(-5y-19)+5y=-7
-15y-57+5y=-7
Add 57 to both sides:
-15y+5y=50
Add like things (the y's):
-10y=50
Divide both sides by -10 to get y:
y=-5
Substitute -5 into x=-5y-19:
x=-5(-5)-19
x=25-19
x=6
Your answers are x=6, y=-5.