The nearest(), precede() and follow() functions find the single nearest/preceding/following range.

Is there a similar implementation and/or easy way to find an arbitrary number of corresponding ranges, e.g. the 5 preceding ranges?

There's the unexported GenomicRanges:::findKNN(). It finds all k nearest neighbors. I think it could be modified to just return the preceding/following ranges. There's already an option to ignore overlaps. If it's useful let me know; maybe we should clean it up and export it.