5 naps is a good number. My baby will be 3 months on May 8 and she takes about 4 naps a day, sometimes 5 if she’s very tired. I think it’s normal, they sleep about 12-15 hours total in a day.
Sleep needs shifts with the 4 month regression. Part of why it's so hard for so many families is they expect the same amount of naps and night sleep when it usually gets cut by 2 hours! So while this is your norm now just keep this in the back for it/when your kid does less naps or less night sleep. So for now if it's working enjoy all the extra sleep! Once it's not working then you may need to change naps around 😊
If she is tired, let her sleep :) she has a routine and this will change as she gets older. My son was never a napper during the day and if he did sleep was only 20min he slept a better at night but still was waking up for feeds which is fine. It’s completely normal :)