The very first thing you should do is go weigh your Explorer at a scale and subtract that from the GVWR. That will give the true, actual and use-able payload number. It the payload figure you are quoting isn't this one, it's going to be inflated. The factory payload wt. is for a full tank of gas + 150 lb driver so you have to add in the DW, kids, pets, in-laws, groceries, firewood, tools, etc, plus any add-ons or options. In the end, you'll find you don't have anywhere the payload capacity left over you thought for your trailer.
Towing capacity is THE number all the TV manufacturers like to brag about, but it's only part of the picture. If you don't want to overload your TV, you need to look at the actual payload as well. There's the receiver hitch max. capacity to check also.
You want to have your WDH set up correctly otherwise the rear TV (drive) axles may be taking too much weight. Get yourself some sway control otherwise you're in for a wild ride when passing trucks, getting passed or in gusty wind situations. My own personal engineering reviews led me to the Reese dual cam. It's self-centering which I like and is under $500 if you shop around (integral sway control). You've got a TV on the shorter side which will be more difficult to handle in wind.
Do NOT use the factory dry tongue weight for ANYTHING. The actual wt. is going to be higher, and possibly much higher, like around 1K lbs as stated above. WDH hitches have different weight ratings of spring bars. Try not to order ones in advance unless you are positive you know what the actual tongue wt. is.
Do NOT go by any dry weights for anything useful. They are pie-in-the-sky, fairy tale numbers. The RV manufacturers use them for trying to outdo their competition on weight. Actual weights are always higher, and often MUCH higher. Beware of actual trailer weight vs. it's GVWR. Factory options aren't included in the UVW (dry wt.) and neither are dealer installed things like propane tanks, batteries and spare tire. Then all of your cargo and any mods. (like television, eg.) all add more weight. End result is a lot more weight than you ever expected. You can run out of cargo carrying capacity before you know it (like on ours). You may not be able to travel with one or more full tanks of water (fresh, black, grey) without overloading the trailer or more cargo for a long trip.
If you have a tow capacity on the lower side and have something like an Explorer, it's even more important to pay more attention to anything to to with weight as is it is easy to end up overloading your TV. Once you have bought a trailer, you are stuck with it and can't return it to the dealer because you found out it's too heavy. No-one here is trying to alarm you - if you come to a forum like this, you'll end up finding out what the truth and reality is, compared to some "sure you can tow it no problem" pitch from a dealer and/or the manufacturer. They conveniently do not discuss wt. capacities and in particular, payload capacity. All they want to do is get an RV off their lot. So - shop smart, tow smart and camp smart!
If all you have to go on at the moment is your max. tow capacity, you *can* use a rule of thumb estimate of max. trailer wt. you can tow of 80% x your 5,000 lbs = 4,000. That isn't going to be much of a trailer for a family of 5. Some even say to use a percentage as low as 60% because of all the abundant wt. issues with trailers and TVs these days. A trailer this small isn't going to be very suitable for 5 people, and what about when he kids grow up?
Our last (and first) trailer was 20' long and had a dry wt. of 3800 lbs. Loaded up and with all the "mandatory" things like propane tanks, batteries, jacks, chocks, sewer fittings, etc. plus cargo, it weighed 5,000 lbs. Our old F150 V6 had a max. tow capacity of 5500 lbs. It was awful on hills and running really hard much of the time. On the I-5 driving south to Grants Pass it was painful. Could only make 35 mph and we were on the right side curb lane with the semis. And that was with only 2 adults. Driving the road from Grants Pass to the Oregon coast (and dipping into Cali.) was the worst white knuckle ride ever. I've driven some of the roads around Norcal (in a car) and they can be nasty! Am trying to illustrate why you don't want to tow a max. weight trailer plus the family and other stuff in your Explorer. You may want to just look at a pop-up/tent trailer.
Money notwithstanding, I would really suggest, as I think others do, that you move into a bigger tow vehicle with more towing capacity. You'll quickly find you wish you did plus the fact that your family is probably growing and you'll need more room. If you do get a trailer, I really recommend something with a slide in it so you aren't bumping bums all the time. If you do buy something to suit your current tow vehicle, don't forget to think about what you'll get for it when you go to sell it. Despite what you think, you'll be wondering what a bigger and nicer trailer is sooner than you think. Happened to us despite what we told ourselves and everyone else. And we upgraded to a 3/4 ton truck and are happier than a pig in !@#$. It's camping season now - perhaps rent something to try it out?