A possibility is to use RF on each year separately (assuming the responses are rolled up into one yearly count). That should give you 5 sets of possible predictors. From there, it depends on subject matter knowledge and the question you need to answer. You could pick out the intersecting set of predictors (those that are selected for every year) or the union set (those that appear at least once). However, it really depends on what the objective is - best association (which is what RF will give you) or possible relationship with individual predictors. Not to be ignored are interaction effects, which likely are not accommodated in the RF dataset.
I know that isn't much of answer, but this is more art than tech, and it is going to depend a lot on what you do know and what you want to know.
SteveDenham
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