No, in fact it could make matters worse.
A magazine size limit does not hinder a mass killer -- only the person who has to defend themselves against that killer.
Someone who's intent on committing mass murder has all the time they need to acquire as many ammunition magazines, which can be switched out in a fraction of a second, as they want beforehand.
The person who has to defend themselves against such an attack does not, because the threat is immediate. If they have a gun handy, at best all they will have with it is a single magazine. If that magazine has only five rounds, that's all the defender has, while still having to face a killer who has as much ammunition as they want.