I don't know how any changes to STR in A5E can be implemented and still be 100% compatible to basic 5E.
Personally, I would delete CON and put it's mechanics into STR.
As mentioned, min STR for almost all armor and weapons would also be good choice.
then when you have min STR for all weapons, all melee weapons can use either STR or DEX for attack and damage.
I.E: you have 20 dex: +5 to attack and damage;
If you have 8 STR, you might only use dagger for 1d4 damage, but if you have 16 STR you could "finesse" ¸1d10 weapon.
same for bows/crossbows;
2d6 damage bow might requrire 20 STR, while 8 STR bow would deal 1d4 damage.