You are correct deep sleep is designed to minimize power requirements typically when using battery power to extend the up time and life of the batteries. I have a pool temp monitor that sleeps for 30 minutes between readings that is powered by 4 AA batteries. It's been running for a couple of weeks now. I may eventually convert it to solar power through rechargeable NiCd's, but so far it's been running just fine on 4 AA's.
If you do not want to, or never need to sleep because you are running say from a wall wart (plugin power), than remove any code that supports the sleep, do your initialization in setup() and put your working code in loop(). If you are doing periodic updates to Particle, just use delay() as Pete suggested.
In your original code (were you test pin 5 low to enter sleep) you had set the pin mode for pin 5 as INPUT_PULLUP. This means pin 5 was always HIGH (unless you externally pull in to ground). Because it was always HIGH you never entered sleep but did enter an empty loop() where you code remained until the next power cycle. It's near impossible to upload a sketch when in this state.
If WAKE was connected to RST from the start and you entered sleep, the Oak should have reset when the sleep time expired. If you entered sleep without this connection and connected it before the sleep timeout, it should have reset. If you connected it after the sleep timeout, then I believe it would not wakeup the Oak as the timeout already occurred and attempt to trigger reset would not work because there was no connection between WAKE and RST to facilitate the reset. Make sense?
Hope this helps.
No worries. Don't mind helping those that want to learn and actually do. Many grab code examples without trying to understand what is going on or what the intent was, then sometimes struggle to figure out why things don't work as expected. My general advice when using or modifying example or someone else's code is to do a 'code review / walk through' first and ask why this and why that, until you have a good handle on how it works. My second piece of advice, to be applied if the code will be production (shipped) code, is to beat the living blank out of it and try to break it in any way you can think off. Sorry for the preachy part. Not directed at anyone but myself. Just the way I approach software. That said, I'm not perfect.