Protein shake mid-morning

amyup

I have been eating small paleo every 3 hours but my mid morning meal is a protein shake (I know it's not paleo). Is that a waste of good protein since I sometimes work out in the a.m (around 5 am and I have the shake around 10 am) but I mostly workout in the early evening? Is it too late for the morning working and too early for the evening workout? Is it doing me any good?