Since we want the ratio a:b divide through by b:
(2a/b-3)/5=(a/b+1)/3.
To make it look a bit easier call the ratio r:
(2r-3)/5=(r+1)/3.
Now cross-multiply:
3(2r-3)=5(r+1),
6r-9=5r+5,
6r-5r=5+9=14, r=14.
So a:b=14:1
CHECK
a/b=14 so a=14b.
Substitute in the original equation:
(2(14b)-3b)/5=(14b+b)/3,
25b/5=15b/3, 5b=5b, which is true sports the ratio is correct.