I'm studying kanji and just got to this character recently. Kanji dictionaries all over the internet list "also N5116" as one of its meanings but what exactly is that N5116? I tried googling it a bit but only found the same dictionaries.
As mentioned by Earthliŋ, these are indices in the Classic Nelson kanji dictionary. A quick search tells us that N5114 corresponds to the index N6610 in the New Nelson dictionary. Here's an image from my New Nelson dictionary. N5116 presumably corresponds to N6612 then.
When I look for pages that mention this, it looks like they're using outdated versions of kanjidic...
I think that N5116 is a dictionary index for the "Classic Nelson", i.e. The Original Modern Reader's Japanese–English Character Dictionary: Classic Edition by Andrew Nelson, so that N5116 means "character 5116 in the Classic Nelson".
The actual kanji 響 seems to be 5114 in this dictionary (i.e. N5114 in the notation used above) and I'm guessing that N5116 is a variant of the same character. Unfortunately, I don't have a copy of the Classic Nelson to check what variant that would be...
In any case, I think "also N5116" is an annotation to the kanji 響, meaning that 響 can also be written in some other way, and somewhere during database crunching got listed as a meaning, which it is not.