hypergeometric test can definitively be tricky.
What are the function of sublists... The sublists represent features (e.g. genes) sharing a particular concept. The basic idea behind is that you are able to better understand your list of significantly regulated genes.
One can also do a focus analysis of the genes belonging to a particular concept. For example looking specifically at those genes across your different conditions using a heatmap coupled with a hierarchical clustering etc...
5% FDR is the consensus for the significance level. But p-value are not the only statistical measure of interest and are highly sensitive to sample size. To conclude this is only one step in your analysis it helps believing in your analysis but you will have to consider the context and think about what biological validation you should perform to make your point.