It isn't extreme. It is a correct reasoning. One can analyse such
data using a multivel model (complicated), or some kind of
repeated measures-analysis, or aggregate each individual's
5 responses in an appropriate way and use the aggregated
measure as dependent variable.
That depends on the nature of the measurements
and on the research question.
E.g.. if one has 5 yes/no responses from each partcipant,
then it could be useful just to count the number of "yes"-
responses and use them in the analysis. I am not sure
what exactely your response variable is/response variables
are here, but maybe you can aggregate the 5 responses in
such a way that it suits your purposes.
Alternatively, if response sets are different from each other
and all 5 sets are the same for all participants, it might be
feasable to perform 5 analyses, but I am of course not sure
about that because I am not familiar with this area of research.