KitchenAid mixer,model # KG25H0XMC5 will not turn on.

SOURCE: Grinding Noise

If it's metallic sound you are loosing teeth on a gear or two.  This is caused by lack of lubricant or simply fatigue of the material of the gears.  Don't use it, you can get metal flakes in your food.

Take it in to a repair shop and have it fixed.  The money spent is well worth it because if done correctly will last another 12 years.

SOURCE: Kitchenaid 350 stand mixer power problems

I'd check the brushes. The big black screws on the side of the motor casing, easily removed, but becareful when you put them back. Here were some instructions from another site that helped me get them back in right:
The brushes in my model KP50PSBU must be insert in a particular manner in order for it to work correctly. If you remove the brushes and shine a flashlight into the hole, you should see a small detent or "stop" in one corner of the hole. Its a square hole. Match this corner with the corner of the brush which is shaved off. The brush is not square; it has one corner shaved or smoothed down. This allows the brush to fully extend into the hole. If the brush is inserted any other way, it will not contact the motor and will not run.

SOURCE: My KitchenAid Mixer won't turn on

Check your Brushes  or bushings or whatever there called ) those little black things on the side of your mixer above the speed selector and the up/down switch) Check to see if they have started to wear down then i recommend taking it in for service. Good Luck!

SOURCE: KitchenAid 250 Watts; Classic: Leaking Oil

Found this,may be helpful.
Why do I see oil leaking from the beater shaft of my stand mixer?
Some KitchenAid® stand mixers that are not used very often or have been tipped may experience slight oil leakage from the shaft or hub attachment. To avoid the oil leakage, KitchenAid suggests that you run the mixer weekly for short periods of time. Generally, the mixer may lose approximately X cup of oil before repair is necessary. The oil used is FDA approved and is not harmful to consume, should any get into the food that you are preparing.
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SOURCE: Kitchenaid K5A mixer 10 speed only runs on fast, no slow speed

Pull the back off and there will be two screws at the top of the Speed Control Plate and a 3rd screw at the bottom. Tighten the top two screws down. [email protected]. Let me know if it works.