1. Read your 2013 Explorer Owner's manual cover to cover. It will have basic information in a towing section which would answer most of your questions.
2. Read this
2013 Explorer Towing Guide. It will answer all of your questions, and many more you haven't thought of.
The short of it:
1. You must use a weight-distributing hitch, otherwise you are limited to 2000 lbs. Unless you have ordered the very smallest of popup campers, you will need a WDH.
2. Your 5000 lbs max tow rating is for the actual loaded weight of the camper. Since you don't know what that is, a good approximation is 800 lbs over "dry" weight, or 600 lbs over "delivered" weight. Using the GVWR of the trailer is too conservative, IMO, as few campers will ever get loaded that much. But neither should you expect to tow a 4800 lbs "dry" camper, since no camper ever gets delivered or used at "dry" weight.
3. The towing guide refers to typical state laws that often require trailer brakes for any trailer over 1500 lbs. That's good enough for me. But even if your state does not require it, in my professional opinion:
If the combined weight of the 2 loaded vehicles will exceed the tow vehicle's GVWR, then you must have functioning trailer brakes. This is because the Explorer's brakes are only designed to adequately stop the Explorer itself, up to it's GVWR, but NOT it's GCVWR (combined rating, see towing guide). For a camper, that's almost always electric brakes, controlled by an in-cabin electric brake controller.
I highly recommend the Tekonsha "P2" or "P3" controllers as the best bang-for-the-buck. RVWholesalers.com or etrailer.com sells the P2 around $125 and the P3 ~$30 more. They are funcationally identical, but the P3 has a more user-friendly LCD user interface, while the P2 (used to be called "Prodigy") makes do with a more basic digital readout and dots. I have had my Prodigy for 11 happy seasons, used in 3 different tow vehicles. Anything cheaper will not perform as well, nor as easy, nor have such good diagnostics. Anything that performs better will either be prohibitively expensive for the casual camper, or only be available as OEM option (such as the SuperDuty trucks integrated controller...which was designed by Tekonsha!).
Your vehicle may or may not have pre-wiring as part of the tow package. But from what I read in that towing guide, you will have to get additional wiring installed for the controller back to the 7-pin controller, as well as a 12V charge line if you want to charge your camper battery in-route. This is routine work that can be done at any trailer/towing shop. I had my first minivan done at The Hitch House, to tow our popup camper. When we had to replace that van, I did the wiring on our replacement van myself, with a kit from etrailer.com. Our Mounty was all set as received.
Give this thread a few more days. Hopefully someone with a 5th gen will chime in, and let you know whether you have this pre-wiring or not. You can also look at the wiring coming into that 7-pin connector. If there are only 4 wires, you only have lights. If there are 6, then you also have the brake and 12V wire. 7th pin is typically unused (reserved for backup lights).