M.F.
First of all, a 5-month-old that sleeps from 9pm to 6am IS sleeping through the night. Good job! And it's great that he goes back to sleep after the 6am bottle.
If he is, indeed, teething, I'd give him the Tylenol just before bed time. Both of mine had (and still have!) these interruptions every few months for one reason or the other. Generally, we deal with whatever is causing it, it lasts for 3 or 4 days, then it takes another 2 or 3 days to re-establish our previous routine.
You might also note that symptoms for teething and for ear infections are almost identical: runny nose, grumpy, low fever, tugging at ears, not wanting a bottle (or just chewing the nipple when it's offered). With either problem, he might not be drinking a lot during the day, but will finally take a bottle in the middle of the night because he's hungry enough and tired enough to ignore the ear/teeth pain.
One thing I know Babywise says is that hunger is always a legitimate reason to feed, so I would simply offer a bottle when he wakes up and get him back to sleep. If it happens more than a few days, you might want to assess his day-time eating.
If you've started solids, he might not be getting enough milk/formula, so he's really hungry in the middle of the night.
Maybe a bed-time bottle will help. Both of mine did not initially have a bed-time bottle, but then got one around 5 or 6 months old, then dropped it again by their first birthdays. Just make sure he's not falling asleep while drinking the bottle, and you want to brush his teeth-gums so the formula doesn't sit on his teeth all night (shouldn't have to worry about it if you're using breastmilk). We would offer the bottle after bath time and story time, then brush teeth (this was simply letting the baby chew on a little baby/toddler toothbrush), which helped keep the bottle time separate from sleep time.
As a side note: establishing teeth-brushing at this age worked really well for us. We've never, ever had an issue with it with either child (now ages 2 and 4).