Sounds like she needs to grow up some and get on a responsible working adults sleep schedule.Very interesting. 4-6 hours per night just doesn't cut it. Shutting off the internet is a good idea. She likes to "nap"-more like sleeping for several hours when she gets home from work in the afternoon, causing her to stay up late, even though she gets up at 5am for work. I already told her I am putting the fire alarm horn and strobe above her bed. If the flashing strobe doesn't wake her, surely the 90+ decibel alarm will.
If she's coming home from work and falling dead asleep for several hours then staying up all night I would take that as a solid sign that she needs to adjust her sleeping habits considerably.
A typical person's sleep cycles are about 90 minutes long so if you go backwards from 5 AM in 90 minute steps.
Right now it sounds like for her 5 AM is right in the middle of a sleep cycle which is the hardest point to wake up from by external stimuli like sound and light.
I would recomend her trying to take one or two Ibuprofen or Advil PM pills for a few days. Going backwards from 5 AM 6 sleep cycles will put you at about 8 PM which would be a perfect time for her to take the sleep aids giving her a good 90 minutes to wind down followed by 5 solid sleep cycles that should end right about 5 AM.
I bet that after 3 - 5 nights of that the afternoon naps will end and the alarms you have now will work just fine.
If she refuses tell her some crazy clown guy you met online is going to start showing up at 5 AM and tasering her feet to wake her up..