you can get the results from the API histogram endpoint, and then sort the results. here are the daily counts in Tennessee since 2010: http://api.inaturalist.org/v1/observations/histogram?place_id=45&d1=2010-01-01&date_field=observed&interval=day.
so the top 5 days have been:
2019-04-27: 2533
2019-10-08: 1546
2020-04-02: 1426
2019-05-18: 1424
2018-04-28: 1413
UPDATE: