Nitrite level of 5+ ppm

You can do 25% water changes daily to get the levels down...If your nitrites just spikes recently, it going to be a while before they come down. If you still can't keep them down, I would even go to larger water changes daily to make sure that all your fish don't poison themselves.

Aside from that...yes, you just have to wait.

If your ammonia is now at zero, but you still have nitrites, you can re-seed your system. Scrape the very top layer of gravel off a well-matured system. Use a square deli container or refrigerator "serving saver" to get just the top. Rinse it lightly in tankwater and scatter it all over the surface of this tank.

A pinch of salt per gallon will help the fish. The chloride ion (it could be potassium chloride just as well-- or better) inhibits the uptake of nitrite by the chloride cells in the gills. Nitrite is very stressful.

Keep up the water changes. This is an emergency!

I'll second what the others have said, and add that you might want to try to keep the nitrite level at or below 1 ppm if you want your fish to survive in good health. Definitely, you need to get going on the water changes...

Jim