No, no, Willie Thorne, this just will not do.
You are either going to have to improve the rhyming pattern of your limericks or stick to the green baize. Lines 1, 2 and 5 should rhyme and so should lines 3 and 4. Well. it does not take a Betjeman to notice that they don't.
Let's see if we can improve matters without changing the thrust and intention of your composition. Actually, the first two lines are fine and could be allowed to stand, but things go downhill rapidly after that...
Firstly, let's lose gig at the end of line 5 and chose another word.....slick would do.
Secondly, the word chosen for first of the pair of rhymes in line 3 & 4, back, is too close to the -ck sound at the end of line 1. Let's go for some entirely different rhymes..... a random choice might be forgotten and rotten.
That would enable a reconstruction that read like this:-

There was an old man named Dick
who thought that mud wouldn't stick.
Would he let be forgotten
Reviews that were rotten?
No! Career-wise this move wasn't slick.

PLEASE NOTE This reconstruction has only been made in an attempt to improve the quality of the limerick and for no other reason.