It's okay.. alittle tweaking and lots of consistency is in order!
For the next two weeks (or more.. probably not though!), make life as easy as possible. Delay appointments, get togethers etc until he is sorted out and can handle it. If possible, see if your older child can go to a friends house during the day.. makes your life loads easier! If not, then give her lots of activities during the day.. she's 5 years old and probably knows how to occupy herself!
Make his morning wake up always 7 am.. don't let him sleep in past 7 am, it's throwing off the rest of his day and his body rhythms. So while you are supporting him into a new daily routine, wake him up every day at 7 am. Give him his feed.. and then breakfest 1 hour later.
Make his morning nap no earlier than 9 am.. but try not to push the time past 2-2 hr. 15 mins, or he'll hit fatigue mode and will have a rough time settling. Prior to his naptime wind down, do a pre-wind down. Take him outside for a carry walk.. Start this around 8:45.. a little walk about looking at trees, feeling the wind etc.. nice and soothing. This will stimulate the "calming" hormones.
Then do a consistent wind down routine. Make sure his sleep environment is conducive to sleep-- dark and low stimulating.
You mentioned you are doing pu.pd. Awesome.. that is a great tool to teach sleep and continue to instill trust. It's hard work, but so worth it! A better alternative to CIO and Controlled Crying. Make sure you are doing it correctly-- Tracy's new book has all the tricks and how-tos for pu.pd and I always recommend it.
Keep his feed around 11:00, depending on when he shows his signs of hunger. And lunch 1 hour later.
His next nap would 2-2.30 min. from his morning nap wake up. Again, do a pre-wind down and then a wind down routine. Make sure he is going into his bed awake but drowsy and do pu.pd if needed.
He'll probably be ready for another feed around 4:00 ish. And may need a short nap around 5ish.. that's typical of 5 months old. Make this a stroller walk, car ride type of nap. I know this sounds counter-babywhispering.. but what you are doing is making a distinction between his morning and afternoon nap, from his late afternoon cat nap. You want his body/brain to recognize that his naps in his crib, which are motionless and depend on his ability to self soothe, to be longer than one sleep cycle (longer than 45 mins.), whereas the late afternoon cat nap, is a motion-induced nap-- a completely different kind and quality of sleep, lasting no more than 30 mins, and will give his body just enough energy to make it to bedtime.. which will probably decrease his fussiness and crankiness in the early evening (if you are experiencing this).
Dinner upon waking from his shortnap.
Start his bedtime routine after 6 pm.. and aim for bed by 7 pm. Anything later, will take away from his night sleep and affect the quality of his nightsleep and his pre-dawn sleep (4-6 am).
Using pu.pd will really help you teach him to take good naps and have good night sleep. Make sure he is going into his bed at night, awake but drowsy. Sometimes the pre-bed top up feed can induce sleep, so if he falls asleep during the feed, wake him up. Soon he will associate this feed with just feeding, and going into bed for falling asleep.
It does take time to straigthen out his daily routine. Some days will be great.. some days will be wonky and messy.. don't worry. This is completely normal. And keep reminding yourself that his days will improve.. he just needs support and guidance towards havng great days!
Hope this helps and let us know how it;s going!