The best spell casting party in the game is 1 element+summoning per party member and that is only if you are willing to respec later on.
No, that's emphatically incorrect. You should grab at least two different magical schools per character because of immunities. You can also take summoning as a third school if you want, or even a third magic school - just don't expect to max all the schools.
Additionally, just because something might be the most efficient way (and I disagree that single-element mages are at all efficient), doesn't mean it'll be the most fun. There's no need to run 4 summoners.
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Now that said, while it's okay to splash a few points into different schools, I think 5 schools is too much. If nothing else, the Memory requirements alone will be fairly substantial if you want to actually use those schools. You can probably handle three schools with a very limited splash. Also the more schools you splash into, the more onorous your Memory requirements will be.
You did have a reason, but I still have to question the utility of a single high-STR character in a party of mages. It might be better on occasion to use Peace of Mind and Strength potions for the things you need to open. But if you think you can manage it, go ahead.