Every layman understands what “5 times less” means.
It means that if an event has a 50% chance of happening (e.g. an unvaccinated person catching COVID given a certain exposure scenario), and another event has a 10% chance of happening (e.g. a vaccinated person catching COVID given the same exposure event), then it makes sense to the average person that the first event is 5 times more likely than the second event.
It also makes sense to the average person that the second event is 5 times less likely than the first event.
The fact that a mathematician would never use the latter terminology is irrelevant. A mathematician insists on precision when converting mathematics to language. The average person doesn’t care.
So, in the context of attempting to persuade anti-vaxxers that the vaccine actually does reduce the chance of infection, the use of the phrase “5 times less likely to be infected” is perfectly valid, and will be understood by the intended audience. Whether it is believed is another story.