I'm not quite sure this makes sense. Just because one shaft feels better on a certain club doesn't mean that it will feel just as good on a different club. I think a range session is in order for you, but I don't think that having a shaft longer than stock (assuming that you are of normal height), will be any kind of positive on that club. That's more of a long drive mentality.
Side note: swing weights are a thing, and if you mess with them, they can mess with you.
A suggestion but this would require you to have somebody you trust as a caddie. When you ask for a 4 or 6 iron, they would give you a 5 iron and you wouldn't check the number at the bottom of the club. It seems entirely psychological to me and after a few rounds you should be OK.
The other option is to go to a range and just hit a couple of hundred balls with the 5 iron only. Nothing else. Hopefully muscle memory will improve the strike