I have run into this and not just on the Note 5. It appears some of the stock SMS/MMS apps get a bit choked and stop sending, and in some cases receiving, until you do a clean out or reboot/restart.
I switched and set GMessenger as my default and have had far less issues. Others have used other choices with the same.
Looks like there may be something with the stock app.
Not just Samsung. Have seen this on HTC also.