Age of travel trailer

A lot depends how mechanically inclined you are. I bought my Jayco within your budget including the wdh and it was in excellent cosmetic condition (a big reason why I picked this one). That said, it needed a lot of little things done to make it ready. Other than new tires, none of it was expensive, but many of the issues might catch out someone who might not have a lot of "fix-it" experience.

A prime example was a leak around the air conditioner. The clueless previous owners had gooped up all around the unit with everything from latex caulk to silicone to expanding foam(!). Fortunately, it was stored indoors so there had been very little actual water intrusion. All that was required to fix this was to remove all the cr*p they tried, verify that the gasket was good and properly tighten the unit down. No more leak.

It had a brand new battery, but nothing worked. Fuseholder at the battery was corroded. Easy fix.

Toilet had been disconnected because it leaked. Replaced the valve for less than 20 bucks.

And so on. I do all my own work (including mounting the new tires) so none of these issues were a big deal or costly. I now own a fully functioning, large, comfortable trailer that most people who see it don't believe it's a '94. (Maybe someday I'll post some pics, but I'd have to wash it first;))

For just a 5 day trip and "maybe" occasional use later, and with a, "$3-5K range," I wouldn't go with an RV. You will have a hard time finding anything that is even serviceable for that price.
Anything that inexpensive will need lots of work (tires, etc) to make it safe and useability is another issue (electrical and plumbing issues). Also, pulling a travel trailer will double your fuel usage

Consider long days of driving and motels for this trip.

Maybe others will give you a different perspective on your plan.
Good luck with your move.

Age is really unimportant. What you want to look at is condition. Is there any signs of water leaks? How about tires? Do all the appliances work? In that price range these are going to be the biggest dangers. Even if the tires look good, you will probably want to replqce them based on age and brand.

Consider a tent trailer. They can be found on craigslist and other places pretty cheap, can be towed by most any vehicle are light and very easy to resell at the end of the move.

There are some basic safety items you should make sure are in place before you buy.

1. Make sure there is no rust on the frame that would weaken the structure
2. What kind of shape are the tires in? If they are old, worn badly or have sidewall cracks, you'll probably have to invest in a new set before towing.
3. Make sure the hitch and all the mechanisms that go with it are in sound shape.
4. Can you have someone pull the wheels and check the brakes for wear and proper function?
5. Do the holding tanks leak? Do the holding tank valves work properly?
6. Check the roof and interior ceiling for any sign of leaks.
7. Verify that the refrigerator is in working order.
8. Check the furnace, A/C and Stove to make sure they work.
9. Does the previous owner have a maintenance history?
10. Fill the water tank, and turn on the pump. Does it come up to pressure? Do all the faucets work?
11. Pull out the awning and check for excessive wear on the fabric and make sure that the hardware moves freely and is in sound shape.
12. Make sure there are no leaks in the propane system.
13. What kind of shape are the batteries in?
14. Make sure the smoke alarm, propane detector and carbon monoxide (if equipped) detectors are working.

I'm sure others will have items that you should check, but those are the basics. If something needs repair or replacement, it will be a good negotiating point.

My wife and I bought a 1993 25ft Terry for 3500. I've put another 600 or 700 into it, but the end result turned out very nice. We're heading about 4 hrs away this weekend and planning a trip to NM next spring. With properly maintained axles and good tires, it should make the trip just fine. No slide for us. Adds weight and complexity for space that we don't really need.