If the immune reaction in the vaccinated was good enough to avoid symptoms but a few still tested positive then those five are surely not the only ones. What are the chances that a random person without symptoms would be getting tested exactly those days that a very mild infection lasts? Those studies don't observe the subjects with daily PCR or something like that (impossible for ten thousands) and most mild infections remain undiscovered. And mild, hard to discover infections aren't exceptionally rare even without a vaccine, as antibody testing studies have shown again and again.
The pressing follow-up question is this: how many of the control group were discovered with (and despite of) equally weak symptoms? The answer could be anything between many more and many less. If it's more (more discovered very mild cases amongst the placebo group) then the vaccine apparently prevents most infections from happening at all, but if it's less then the vaccine doesn't really reduce the number of infected (and infective), it only prevents bad outcomes (which usually remain undiscovered, even in a phase III trial group).
A vaccine that only prevents bad outcomes would still be very valuable, but only to the vaccinated themselves because it would not create a herd immunity effect. This virus is very good at spreading from a mild case, so if the vaccinated still get unnoticeable mild cases they would still serve the virus as stopovers.