In this SE - and others possibly, I haven't really encountered this problem elsewhere yet - but this SE keeps referring to "new users". Who is classified as a new user? Do new users have low reputation or have only been on the site for a couple of days or months? What classifies a new user from another user who has been around for a while?
Would I be considered a new user?
This is an example of where it can be seen:
In the specific cases you mention - the First Posts and Late Answers review queues - there are strict definitions of "new user".
The First Posts review queue contains posts from users who've never posted on the site before: it literally means first posts. This queue was implemented in 2012; see New Review Queue: First Posts on main meta.
The Late Answers review queue contains answers from users with less than 50 rep which were posted at least 30 days after the question was asked. See How old does a question have to be for it to be a late answer? on main meta, and note that the rep bar was raised from 10 to 50 on 29 September 2015.
In general, there's no strict definition. Different people use the term "new user" in different ways, according to their own reputation and time on the site. Some people would see me as a new user, since I've only been here since 2014; others probably see me as one of the mainstays of the site. It's all subjective. There are only two possible general definitions I can think of:
users with less than 10 reputation: according to the help centre, one gets "new user restrictions" removed at this point (though I still think of some users with >1k rep as being new)
users who've been around for less than 45 days: this is the definition used by the new users tab in the user list (thanks to @anaranjada for reminding me of this)
Would I be considered a new user?
I would say no. You have over 5000 rep, and you've been a member of this site for longer than two of the moderators - you're no noob :-)
