It sounds like you've been trying to be open to suggestions from the parent in trying to solve your problem. If communication is really breaking down and the parent still wants what you would consider way too long between feedings,it might help if you research feeding spans in some books or on the internet and have documentation on why you feel this time span is too long and what effects it could have on the child. I think it is "normal" for a child to go between 2-4 hours between feedings at 5 months depending on how much they eat at a time, when nap times are, and if they have a comfort items such as a Nuk, blanket,or use fingers. Also, have solid foods been introduced yet?
I went to www.babycenter.com and found this in an article about schedules for 5-6 month old babies:
As you're creating a schedule for your baby, keep in mind that at 5 and 6 months most babies need:
• 12 to 36 ounces of breast milk or formula in a 24-hour period. (Get specific tips on how to tell whether your baby is getting enough breast milk or formula.) Most babies start solid foods at this age, though they'll still get most of their nutrition from breast milk or formula.
• About 14.25 hours of sleep in a 24-hour period — this includes nighttime sleep and naps. Two naps during the day (morning and afternoon) is typical, though many babies will still take three naps.
Schedule 5: A formula-feeding stay-at-home mom of a 5-month-old
Editor's note: This schedule is a parent-led routine
6 a.m.: Jack wakes up and has an 8-ounce bottle.
6 to 7 a.m.: Playtime with Daddy.
7 a.m.: Cereal and pureed fruit (baby food).
8:30 to 10 a.m.: Naptime.
10 to 11 a.m.: Playtime.
11 a.m.: 6- to 8- ounce bottle and jar of fruit (baby food).
Noon to 2 or 3 p.m.: Naptime.
3 p.m.: 6- to 8-ounce bottle.
3 to 6 p.m.: Playtime.
6 to 6:30: We go for our evening walk.
6:30 p.m.: Cereal and veggies (baby food).
6:45 p.m.: Bath time.
7 p.m.: Prayers, 8-ounce bottle, brush his teeth.
7:15 p.m.: Bedtime — Jack sleeps until the next morning.
Schedule 6: A formula-feeding working mom of a 6-month-old
Editor's note: This schedule is a combination (parent-led and baby-led) routine
Isabella is in daycare and has a pretty set schedule.
6 a.m.: She wakes up, starts talking in her crib.
6:15 a.m.: Talking louder, letting Mommy and Daddy know it's time to get up.
6:30 a.m.: Daddy feeds her a 7-ounce bottle and then plays with her and kisses her while Mommy showers quickly and gets ready for work.
7 a.m.: Dress Isabella and leave the house by 7:15.
7:15 to 8 a.m.: Nap time on the way to daycare.
8 a.m.: Kisses and goodbye to Mommy, who goes to work.
At daycare, she spends time in an activity saucer, looks in the mirror, plays with friends, and rolls around on the floor. Sometimes they take her outside to enjoy the fresh air.
10 a.m.: One jar of stage 1 baby food, either vegetables or fruit.
10:30 a.m.: She has a 4-ounce bottle.
10:45 a.m. to noon: Playtime.
Noon to 2 or 2:30 p.m.: Nap time.
2 or 2:30 p.m.: She has a 6-ounce bottle.
After that, she listens to stories and music, plays with friends, and goes outside if the weather is nice.
4:30 or 5 p.m.: Mommy picks up Isabella.
5 to 6 p.m.: Naptime while on the way home.
6:30 p.m.: She has some rice cereal mixed with formula.
7:00 p.m.: Playtime with Daddy while Mommy makes dinner for the adults.
7:30 to 8 p.m.: Bath time and tummy time with Mommy.
8:30 p.m.: 6-ounce bottle, then cuddle with Mommy or Daddy till she falls asleep. She sleeps through the night and we start all over again the next day!
Just to give you an idea of what some other parents do. If all else fails, and you feel the child is truly hurting from not being fed, I would ask her to bring in a note from her doctor/pediatrition (possibly with a phone number so you can talk?) on the need for waiting so long between feedings, especially if it's more than 4 hours without a nap in between.
Hope this info helps.