Looks like it's just mini-cycling for some reason. Mini-cycles settle down after a few days, generally speaking. There may not be any particular need to worry right now, but I'd get on top of the big volume water changes and start some more regular testing, maybe step it up to twice a day and change as appropriate. Your nitrites need to be much less than 1ppm, and at 5ppm a 25% water change will only bring it down to 3.75, which is still dangerously high. I'd confirm the current levels again now, and then go from there.
Let's say they're at 4 for the sake of ease of calculation: two 50% water changes one after the other would bring it down to 1ppm (which is still too high, but better than 4). Better yet would be two 80% water changes, which would bring it to 0.16, which is a much better place to be going on from.