I have a galaxy S5 Neo and just today I started having problems with it.
Hi Quinton, I looked at your SMS logs, and do not see any delays in there. The system shows at what time the text was received by the SMS relay, and at what time it was successfully pushed to your phone, and the longest delay I see is 23 seconds. Most text made it under 5 seconds. That means your phone receives the texts instantly, but for some obscure reasons did not display them right away. A power off/on like rikkster suggested should help. If not, this can happen when your phone memory is getting low. Try to delete some unused app, or to clear the cache of your phone.