I remember those days with my first ds... It is so exhausting
Firstly the 40min naps are your main problem & the 3 /3.5 hourly routine in the day time, at 5months, your lo should be feeding at 4 hourly & that SHOULD help with the naps.
Until your lo masters at least one day nap of 1 hour or longer, I think given the regular wakeups that is the only solution I can think of, sometime around the 4/5 month mark the longer naps clicked for my ds when I started holding out the feed times longer. sometimes I had to sort of do feed, activity sleep, activity, sleep, but eventually I got there. It may be that your lo has a shorter or longer awake time & so that is causing the short naps, watch for his tired signs rather than the clock & see if you can get an idea of how long his awake cycle is (at 22 weeks I'd be guessing at it being around 2 hours 15 mins) & feed every 4 hours not on waking