I have a LG dryer model DLE5932W that will not shut off on its own

If its a newer dryer, they have moisture sensors that determine if it should shut down early or stay on longer if needed. Let it run the extra time and see what happens. If it keeps doing it, then the sensor is defective.

Could be over heating and the unit shuts down till it cools off. Check the dryer vent line for clogging all the way up to the vent by the roof. Bet it is clogged some where and that is the cause of your problem.

SORRY TO HAVE TO TELL YOU BUT Dryer runs then shuts down wont start up for an hour:
Bad motor windings

Sounds like loose belt. If the drum spins by hand, it's almost guaranteed to be a bad belt.

drum rollers/glides:

http://www.partselect.com/dryer+dryer-tears-clothes+repair.htm

this could be operator error please hear me out...... when wash bath towels you also put in wash cloths and hand towels .... there is a sensor in dryer drum shroud in front of lint filter to metal silver strips when the clothes are tumbling they sweep across this sensor telling the dryer heat to stay on and continue to dry.... if th small wash cloth sweeps it first before the bath towel then u get the same results as your describing just like if you were waqshing colors load like cotton tshirt and blue jeans the tshirt is going to dry way faster than blue jeans so if the tshirt sweeps that sensor first the dryer going to shut off we have to sort our clothes to thickness ans same size articles just try it once i bet your clothes are dry when cycle completes

Heating element is bad

You have a computer control board problem and needs to be replaced.  The internal program has a problem and won't time down properly.

THese diagrams may help some

http://www.pcappliancerepair.com/model-display.php

Dryer NO Power
You really need a volt / ohm meter to check for Continuity & Volts
Its well worth the investment... $15.00 bucks give or take a few
I would check to see if you have 220v to back of dryer where the cord mounts to dryer,
If dryer is getting only 1 leg 110 volts instead of the 220 will it not heat.
Check themostates & heater for Continuity... Most models, Now have a..
Hi-limit fuse that need to be checked for Continuity and replaced if bad
if you dont have a ohm meter you can hook the wires together
with a small piece of wire and by pass the themostates and hi limit fuse to see if thats the problem or not

I'm sorry to hear of your problem with your LG dryer. I have one as well and it works very well. I found my owners manual. It has a web site WWW.LGSERVICE.com. They also have a toll free number 1-877-714-7486. Perhaps either of these will help you find an answer. Good Luck