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The one-sample t-test is a statistical hypothesis test that is used to see if an unknown population mean differs from a given value.

When you use a normal distribution to do a hypothesis test of a single population mean (commonly referred to as a $z$-test), you take a basic random sample from the population. Your sample size is more than $30$ or the population you're testing is regularly distributed.

Given: Hypothesis test of a single population proportion

When we find that the the number of success $np$is less than $5$, then it is not appropriate to perform the hypothesis test as we require $np>5andnq>5$in order to perform the hypothesis test.

If we want to perform a valid hypothesis test, then we should thus increase the sample size (such that the number of successes in the sample increase as well). That is, more data should be collected if we want to perform a valid hypothesis test

The hypothesis test will not be performed, and the sample size will not be increased.