Well you have just blown the bragging rights of all other Andersen Ultimate Connection of how it solves chucking in a 5er!!
Now to the point, what is your pin weight percentage? Best towing at 20% to 25%, most find closer to 22% is a good spot.
My guess is that you are pin lite, so that the 5er is trying to rock back and forth on the axles.
Is your FW tank forward of the axles, if so try filling it full and see how it tows. You likely need to get pin over 3,100# and it will get smother. To your question on 5er shocks, they will help.
Russ & Paula the Beagle Belle.
2016 Ram Laramie 3500 Aisin DRW 4X4 Long bed.
2005 Copper Canyon 293 FWSLS, 32' GVWR 12,360#
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