Mac won't allow me to add any email account On OS High Sierra 10.13.5. Allows me to write account name, add password, but won't finish task, just stays on next but not frozen. Have tried to delete relevant terms from keychain.
Usually when this happens, it’s a temporary issue on the server side. 

I would remove the account and do these three things:


Set your Mac clock to the internet to be sure ssl and certificate timings match. 
Log into webmail and be sure your account is not locked. Look for two factor authentication or the need for a second password for that account. Those often cause a silent failure. 
Set up only one item at first. Adding five items mail, contacts, calendars, notes, reminders means that all five of them have to be set up in the not time out.  If you can get one to set up and saying and then leave it for 20 minutes, you might then try to add the second and the rest one by one.