Hi! I'm the mom of four (one year old, three year old twins, and a six year old) who were all EBF. Your five month old seems to have a great daytime routine (the wake, eat, sleep, play schedule seems very normal). The clock-like schedule will come when he is a bit older.
My one year old took two or three naps at five months of age. She would usually go down for her first nap between 8:00 - 9:00 and her second nap around 2:00 (depending on how long her first nap was), with bedtime between 6:30-7:00. She would usually wake up once, twice max, to nurse at night, and wake-up in the morning at about 6:30. The first nap at this age is considered to be a continuation of nigthtime sleep. By about 8 months she took two naps, and now she takes one nap that starts between 10-11 and can last anywhere from 2-4 hours. For my little one, putting her back in her crib (instead of having her sleep in our bed) is key to getting her to sleep well at night (she loves to play in our bed and will want to play at 4:00am if she is in our bed instead of her crib). Having a consistent bedtime routine and bed time is important too. Also, from a very young age, I would put her down sleepy, but awake in her crib, so she could fall asleep unassisted. Now she is usually able to put herself back to sleep if she wakes during the night, and usually wakes just once to BF.
I would highly recommend the book "Healthy Sleep Habits, Happy Child" by Dr. Marc Weissbluth. It has been a wonderful resource for me and is guaranteed to help you with establishing nap and nightime schedules with tons of troubleshooting info too. Good Luck!