How do sectors work? Are they controlled by the player or controlled by the AI. It was unclear when reading the wiki. When I reach my 5 core world limit, and want to expand, should I just add a sector instead?
Core Systems are the systems you are controlling directly. You can control more than your 'cap' - just like you can technically go above your 'fleet cap', but it comes with penalties to all energy and mineral income that can become prohibitive.
A system stops being a Core System if you put it in a sector. You can create a sector in any continuous shape you like, then the AI runs all of the planets and any mining outposts you assign to it. You cannot put your capital planet into a sector. You cannot manage those planets directly at all - no upgrading buildings, moving populations, or anything of that nature. The sector collects energy and minerals from those planets, and you set the 'taxation rate' at either 0%, 25%, 50% or 75% - and that is the percentage of net energy and minerals produced in that section that winds up in your coffers. Anything not collected is used by the sector to build and upgrade facilities on the planet.
There are a lot of complaints about sectors, mostly rooted in the fact that the AI is dumb.
Some tips;
Because you only get a max of 75% of the resources produced in a sector, you generally want direct control of your biggest, most developed planets.
For the same reason, and because the cap specifically counts systems and not planets, you generally want direct control of any system with multiple lucrative inhabited planets.
Because the AI is kind of dumb and won't develop a planet very quickly, you generally want direct control of your newest, least developed planets.
Because sectors without inhabited planets don't count towards your core systems controlled, you generally don't want to put them into sectors unless you have to in order to keep the sector continuous.
Anything else can typically be crammed into a sector. A friendly note - the number of 'moves' the AI makes per in-game day is limited, so smaller sectors tend to be better managed.