I have a wall outlet in a bedroom which doesn't control anything. I would like to find out which outlet it is wired to, if any, so I can plug in a light in and turn it on and off with the switch. How do I test all the outlets in the room to determine which of the five outlets it is?

This seems obvious, so maybe I don't quite understand what you're trying to do, but try this: First turn the lamp on and make sure it works. Then plug the lamp into the first outlet, and see if it comes on. If it does, try flipping the wall switch to see if it goes out. If it goes out, you've found the outlet controlled by the switch. If it stays on, then move to the next outlet and repeat. By the way - it's possible that the wall switch controls only one of the two outlets in a duplex receptacle, so test all ten outlets (I assume you have 2 per duplex receptacle).

I might do it differently. Down is usually off, so put it down.
Take a small lamp or night light and test the top and bottom outlet with a known working lamp.

Yes, it's very typical to have 1/2 of a receptacle on a switch especially if there are no ceiling lights.

What may be possible is that either when the outlets were installed, or one was changed, the outlet the switch is intended to control got miswired.

Pull out the closest outlet to the switch, you may be able to see just be removing the cover plate, look for a red wire at one or more of the outlets along with a black and white.

Usually a red wire comes from a switch to a switched outlet. One half is to be live constantly and one half to be switched.

In between the two brass screws of the outlet is a small brass jumper that is to be removed when switching half of a duplex receptacle. Often this is forgotten, and if so, the switch cannot control half of the duplex.

If you find this jumper at an outlet that has both a black and red wire connected to the brass screws, remove the jumper by using a small flatblade screwdriver or a needlenose pliers.

Be sure the circuit breaker for these outlets is off before opening the covers and pulling out the outlets.

It's also possible that the switch controls more than one outlet, such as on both sides of a bed, for lights on night stands.

Someone may have forgotten to break off the Tab. An Electrician might check power to both sides of the switch in the on and off positions, if both sides of the switch are always live, they forgot to remove the tab.

Why not just plug lamp in to each outlet, top and bottom, and turn switch on and off to find out.

Switch may control something other than outlet.