How many months does it take to make 500 gems~~
It depends!
I get a much more fast gems since I joined Neo Monster at new year, and Christmas.
I got lots of bonus gems just from that event, and also gems from the main story.
About 2 and a half months give or take
Heavily dependent on if you have done hellmode etc or how hard you can grind pve events
If you can take part in the 50 gem shrine, you can pretty easily gain 50-100 gems a month depending on what you do of course. Daily quests and login already give you like 40 gems a month, if you do the PvP daily, you will gain 30 more plus all the rewards that come with wins and RP. Also PvE events give a lot of gems. So I would say 3-4 months with moderate amount of playtime, faster if you have a lot of time and obtain every gem available.
I started my 2nd account before an anniversary and didn’t spend one gem. Within 46 days I was at 500 gems.
A brand new account I could grind to 500 gems in the first month, month and a half tops.