How to tell when the rear end of my '07 Dodge Ram 1500 5.7 litre is going?

It depends on what noises you might be hearing for one sometimes when the differential in the middle loses its bearing it starts to whine kind of a low pitch that will build up with the speed of the truck. It will actually get louder and louder until you cannot even hear in the cab of the pick up.

another thing that can happen is if the axle bearings start coming apart you will notice it as you back off the gas and are slowing down you may hear a rorm rom rom rom kind of sound and when you get up to freeway speed you may hear some loud low pitched almost grinding noises that just dont sound right. and if you back off the gas it gets quiet again you can also inspect the differential and if you find metal shavings you know something is wrong and you can get the rear end off the ground supported on jack stands so the wheels can spin and block the front of the truck real good so in case it drops of the jack stands it will not move take a three foot length of garden hose and listen to the wheel bearings they are either quiet or loud and grinding them slefs to bitty pieces. its always good to check the U joints and make sure the

The only problem I ever had with my 9 1/4" rears were early failure of the pinion bearings. They will start growling as you increase speed, warning you that they're on their way out.