If by standard form, you mean ax+by= c, here is how to solve.
To write the equation in standard form, move each variable term to the left side of the equation and simplify.
y+2=3/5(x + 5)
y+2= (3/5*x) + (3/5*5)
y+2= 3/5x + (3*5)/5
y+2= 3/5x +15/5
y+2= 3/5x + 3
subtract 3/5x by both sides
-3/5x+y+2= 3
subtract both sides by 2
-3/5x+y=1
multiply by 5 to eliminate fraction
-3x + 5y= 5
ANSWER: -3x + 5y= 5
Hope this helps! :)