I observe that y = -3 would be a solution if the equation were not (y+5)/(5-3) + -3/15 = 1/-3 , but (y+5)/(5*-3) + -3/15 = 1/-3 .
It also is written oddly, so I wonder it you had already replaced some of the y's with -3, and the actual equation was (y+5)/(5y) + y/15 = 1/y .
Is that what happened here? If so, then your main error was in replacing y with -3 without parentheses, so that a multiplication changed into a subtraction.
In other words, I guessed right. The solution is y = -3, and substituting as I showed, replacing y with "(-3)", will make the check work.
Note that we ask you to show your entire original question, for exactly this reason: If you show something you arrived at halfway through, there may be a mistake before that point that we could recognize if we saw it all:
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