I'm not early with this one; I was just late with the last time. Here's the list of new groups:
http://www.fimfiction.net/group/205258/new-groups/thread/254924/new-groups-this-week-from-20160519-to-20160522

New groups this week (from 2016.01.09 to 2016.01.16):
http://www.fimfiction.net/group/205258/new-groups/thread/231972/new-groups-this-week-from-20160109-to-20160116

http://www.fimfiction.net/group/205258/new-groups/thread/292571/20-new-groups-this-week-from-20161119-to-20161126

New groups this week (from 2016.03.12 to 2016.03.19):
http://www.fimfiction.net/group/205258/new-groups/thread/242898/new-groups-this-week-from-20160312-to-20160319

http://www.fimfiction.net/group/205258/new-groups/thread/272118/34-new-groups-this-week-from-20160813-to-20160821

New groups this week (from 2016.02.27 to 2016.03.04):
http://www.fimfiction.net/group/205258/new-groups/thread/240420/new-groups-this-week-from-20160227-to-20160304

https://www.fimfiction.net/group/205258/new-groups/thread/318648/19-new-groups-this-week-from-20170506-to-20170513

http://www.fimfiction.net/group/205258/new-groups/thread/269288/new-groups-this-week-from-20160729-to-20160806

http://www.fimfiction.net/group/205258/new-groups/thread/273126/25-new-groups-this-week-from-20160821-to-20160827

http://www.fimfiction.net/group/205258/new-groups/thread/265401/new-groups-this-week-from-20160718-to-20160716

https://www.fimfiction.net/group/205258/new-groups/thread/308260/22-new-groups-this-week-from-20170225-to-20170204

http://www.fimfiction.net/group/205258/new-groups/thread/270589/new-groups-this-week-from-20160806-to-20160813

http://www.fimfiction.net/group/205258/new-groups/thread/286202/23-new-groups-this-week-from-20161022-to-20161029

http://www.fimfiction.net/group/205258/new-groups/thread/281659/17-new-groups-this-week-from-20161001-to-20161008

New groups this week (from 2016.03.26 to 2016.04.03):
http://www.fimfiction.net/group/205258/new-groups/thread/245641/new-groups-this-week-from-20160326-to-20160303

New groups this week (from 2016.05.28 to 2016.06.04):
http://www.fimfiction.net/group/205258/new-groups/thread/257406/new-groups-this-week-from-20160528-to-20160604

http://www.fimfiction.net/group/205258/new-groups/thread/295919/16-new-groups-this-week-from-20161217-to-20161224

https://www.fimfiction.net/group/205258/new-groups/thread/307071/24-new-groups-this-week-from-20170218-to-20170225

New groups this week (from 2016.04.03 to 2016.04.09):
http://www.fimfiction.net/group/205258/new-groups/thread/246761/new-groups-this-week-from-20160403-to-20160409

https://www.fimfiction.net/group/205258/new-groups/thread/311626/18-new-groups-this-week-from-20170317-to-20170325