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It depends upon if the rim was marginaly too narrow for the 10.5" tire. If it was, then it would be too narrow for the 12.5" tire.
If however the rim was sized wide for the 10.5" tire, then it would be fine with a 12.5" tire.
You have to measure your existing rim to be sure. If you are running stock Ford rims, then most likely they would be considered too narrow for proper tire performance.