Short answer for 5 round groups - no no evidence.
Long answer, training in mil firearms handling and in target shooting would teach that good technique at deliberate shooting practice starts with a well rested shooter. Target shooting practice thinking is that you only have a short time holding the rifle on target at each shot, and that the longer you hold the more likely you are to get the wobbles or pull the shot. The more shots you make, the less likely you are to be able to hold on target as long - all other things being equal. So in a partial answer to your question, if the shooter started in a good place fatigue wise and knew what they were about, didn't take an excessive time to run the shot string or rested off the firing line between shots then I'd put forward the argument that fatigue should not be a factor for 5 round strings.
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