In most reputable retailers in the U.K. I think this would be labelled "short-dated" but only just as it still has 5 months to run. It would probably be reduced in price but not by much with 5 months to run. Maybe the retailer in question operates to a shorter timescale, like 3 months, before applying the label.
In reality and given you freeze everything, then what you have bought is as good as say TMax which still had a year to run when you couldn't expect it to be labelled "short-dated"
Always nice to get a price reduction but I don't think you will suffer.
Key to this is whether no short-dated label indicates a retailer who is less concerned for the customer in other ways that might make you think twice about using that source again.
I'd contact the retailer and point out that you were surprised that with only 5 months before expiry it wasn't labelled short-dated.
The reaction you get will tell you all you need to know about whether the retailer is worth using again