It might be fast enough, but will be close.
You most likely will need settings on the DMM to speed it up like fixed measure range, small NPLC, etc.
Given the duration and number of readings, you will need computer to manage a loop of measure and transfer the readings for the 3 hours.
Check out example in appendix B of 2010 manual on the scan card usage.
For the three hour task, I advise you setup a scan list of your 5 channels. This will have lowest overhead/time needed to switch+measure.
Have your PC side software loop: init the scan, bring 5 readings, store to HDD, pause if loop rate needs it, repeat.