It only does if you care for the interaction between the two variables. Since each of your categorical questions has 5 options, the sample size formula needs to be adjusted to both questions if you care for specific answer combinations to the two questions (i.e. as if you had one question with 25 options)

Thanks for the info. The adjustment you talk about is what I cannot find anywhere. I use a simple formula for dichotomous response, because ultimately I can't find a formula for polytomous response. Suppose there is one question with 5 choices. What is the adjustment? Appreciate any help.

Bogdan

I am assuming that the formula you are using allows you to specify the probability of a response (which will be .5 for a dichotomous response). Assuming that all 5 choices have an equal probability you need to change that to .2