more people are participating than we expected
That is good, congratulations :)
and we will definitely exceed this limit
That is something we will be able to solve.
is it 5000 complete interviews, or 5000 started?
It is a soft limit, i.e., we won't bother you if it's 5.500 or 6.000 respondents, and in case of doubt, we will look at the completed interviews (unless someone abuses that to circumvent the limit).
How many (relevant) responses do you expect?