I have a Pmp5000 889406987784 Eurowpower PMP5000 1200-Watt 20-Channel Mixer and Speaker Output A has no output. What has happened?

Check the inserts and pan controls.

If the mixer output shuts down as you describe, some part is over heating and once it cools down you can turn it back until it happens again. This will not be user serviceable. Here is the link to Peavey Support who can provide a service center contact and schematics.
peavey com

The unit has a built in mixer as well as individual outputs. You would need an amplifier/speaker that could receive from teh mixed output jack of this. Use BALANCED TRS cable.

MAKE SURE the cables you plug into 1/4 inch mains are TRS plugs, and not mono cables (TS). The main output 1/4 inch jacks are TRS balanced outputs and if you plug mono (TS) cables that shorts out the ring connector reducing the power by 6 Db. USE ONLY TRS balanced cables for interconnects !!!! Also read my tip on Fixya regarding PMP mixers. If you use 1/4 inch SPEAKER cables or adapters, if you short the SLEEVE of channel A output to ground you can pop the channel A amp. The TIP of channel B is the hot BUT the SLEEVE of channel A is the HOT. The ttip I posted explains why this is and it isn't mention in the Behringer documentation.

If you read the TRUE specs on this speaker it is really a 200 Watt RMS unit. Make sure you are using balanced lines to the speaker XLR or TRS cables. The mixer should NOT be a passive mixer as these do NOT generate true balanced lines. Make sure the mic can't "hear" the speaker or you may be getting supersonic feedback that is above your hearing range that saturates the amp. If *********** can't stand to be ain a 15 foot square room with teh level you are generating, it is TOO loud for this unit to handle.

in your system preferences click on sound and adjust the settings you need.

We can't understand what you are saying... DO NOT PLUG the speaker output(s) of this unit into anything BUT speakers !!! There is a hazard if using 1/4 inch speaker cables that can fry the amp.

You don't specify which model Phonic mixer in question.
Is it a powered mixer ? And are you plugging your speakers into the speaker outputs ? If it's not a powered mixer and you're plugging speakers into the Line Outputs, you're not using a power amplifier between the line outputs and your speakers - this won't work.
If it is a powered mixer and you are plugging speakers into the speaker output connectors and still getting little or no sound, check your speaker cables and the speakers themselves by plugging them into known good amps.

how u hook up a mixer

Probably time for an upgrade to a newer channel mixer. Your mixer is probably not worth fixing, but you could continue to use the mixer side for a while until you decide to upgrade that. If you happen to know an electronics tech, it could be a little project to check the power amp insert jack on channel B, but it wouldn't be worth spending good money after bad when you could put it towards more solid gear.

Good luck.

The dude.