Sure it's believable. It would probably tow a 5,000 pound boat just fine. It would probably tow a 5,000 pound load cinder blocks on a flatbed just fine.
There are many different types of trailers and a hard sided travel trailer is probably, by far, the most difficult to tow. The high percentage of tongue weight, inability to move the tongue weight, large frontal area, poor aerodynamics, and large side sail area make a travel trailer a difficult tow.
Just because a tow vehicle says it will tow 5,000 pounds doesn't mean just any old trailer at all. The same vehicle that might handle a 5,000 pound boat just fine might be a struggling handful with a 4,000 pound RV.
Further, some people have very different expectations. I expect my tow vehicle to be able to maintain interstate speeds up a mountain while towing. Some people are just as happy to be doing 45 with their 4 ways on up the mountain. Some people have never tow within 100 miles of a mountain. I also expect my vehicles to last for 200,000 or more miles. Some people think a vehicle is worn out at 100,000.
That vehicle probably would pull a 4,000 pound RV but I doubt you'll like the experience, particular up a mountain, and I bet it won't live very long.