My Maytag dryer (MED5600TQ is only 5 years old and it started making loud noises, with a burning smell. Dryers should last a lot longer than 5 years.
What is wrong and is it worth fixing?

It is not homework.

Most likely it is dirty and lint deposits have built up, as it always does, in all the air ducts. You will have to take it all apart and clean the drier out thoroughly or it is all for nothing. Every air duct will have to be removed and scraped and washed out to remove baked on lint deposits which bakes on like a concrete lining. This will burn so the manufacturer has installed the safeties to keep from having a house fire. Driers were the number one cause of fires at one time, hence now we have safety fuses. Look at: How to clean your clothes dryer. How to make it hot again. - YouTube (http://www.youtube.com/watch?v=MMP7BW1lLs4) to see how. Also look at these to get an idea about how to clean it: Mr. Appliance Tips: How to Clean Your Dryer - YouTube (http://www.youtube.com/watch?v=iBiRw-KElC4) ; Cleaning a Dryer Vent and Lint Trap - YouTube (http://www.youtube.com/watch?v=yFTZGgVisCI)
Electric Clothes Dryers (http://www.electrical-forensics.com/Dryer/ElectricClothesDryers.html) Dryer vent cleaning prevents fires - YouTube (http://www.youtube.com/watch?v=A6wmD502-xE) and: Cleaning out a dryer with top lint cleanout - YouTube (http://www.youtube.com/watch?v=OBNDbyRm68M&feature=fvsr)
Cleaning out a dryer: By a woman 2 of 2 - YouTube (http://www.youtube.com/watch?v=a73HTFkcB90&feature=relmfu)
When you finish cleaning the drier it is best to also replace the belt, too, because you do not want to have to disassemble it all over again and if the belt is over two years old you should replace it. The noise is probably coming from bearings that have no grease in them, so if they are scored they will have to be replaced. The noise can also come from a missing or worn out felt liner, the belt tensioner, or support rollers. Rarely, the motor bearings can be bad. Dryers must be cleaned every two years.

Note that on most of the videos it does not show them washing out the parts, but this is important because it's the only way to really get the parts clean, just don't get motor wet or the capacitor if it has one. Vacuum out the motor to remove all dust. I would move the drier out to your garage to have plenty of space to work. You also want to check your vent and clean it, also. The vent should have a short run and be straight as possible. The job is really easier than it sounds. There is no shortcut that will work; it has to be cleaned well. Before you re-assemble it make sure to use white lithium grease (high-temp grease) and grease all bearings. Just vacuuming out the dryer a little does little good.
Here are some manuals: https://dl.dropbox.com/u/8010163/Maytag%20Dryers_2.zip