The main concern with configuring your back-end infrastructure devices with IP Precedence value 5 is that the 3560/3750 auto-qos will map this value to Q1 which is ordinarily the strict priority Q.
In most cases auto-qos will also configure or map Video to Q3, you can see this as a majority SRR bandwidth is assigned to the Q.
In order to use the strict priority queue, it has to be enabled on the interface 'priority-queue out', without it Q1 will not be emptied before the others. It will be serviced according to the weight.
With auto-qos Q1 will not have enough bandwidth as it will be assigned to Q3. Therefore you could initially enable priority-queue if not already enabled so that Q1 is emptied first, or you increase the weight.
The next question is whether you are using egress scheduling within the Core? and this conforms to your edge classification for Video?
HTH.
Allan