1995 Dodge Ram Engine turns off

Can you restart it right away? Will it stay running if you hold the accelerator down 1/4"? Was the battery recently disconnected or run dead?

A slipping transmission puts less load on the engine so it is less likely to stall. A battery that is "pretty new" suggests to me you might have a common problem with an easy fix.

When the battery is disconnected, the Engine Computer loses its memory and has to relearn "minimum throttle" before it will know when it has to be in control of idle speed. Until that occurs, the engine will be hard to start unless you hold the accelerator pedal down 1/4", it will not give you the nice "idle flare-up" to 1500 rpm at engine start-up, and it will tend to stall at stop signs or when you shift into gear.

To meet the conditions for the relearn to take place, drive at highway speed with the engine warmed up, then coast for at least seven seconds without touching the brake or gas pedals.

99 out of a hundred times relearning minimum throttle takes care of it. It's a real common problem. In fact, I'm nursing an eight-year-old battery in my '88 Grand Caravan daily driver in the middle of road salt country, and when it's down to 0 degrees, the strain from starting a cold engine draws the battery voltage down enough momentarily that my computer loses its memory and this is the result. If I get out to brush snow off, the engine will stall. Fortunately I have multiple places, including an exit ramp, where I regularly coast for well over seven seconds, so the idle speed problem goes way with little aggravation on my part.

One thing you might look at related to your comment about a slipping transmission is the kick-down cable. There was a lot of trouble with them sticking. That cable gets pulled by the accelerator pedal to delay the up-shifts according to how hard you're accelerating, but under light throttle, spring tension pulls that cable back. When the cable sticks, the transmission thinks you're under hard acceleration, but if you're actually under light throttle, up-shifts will occur at too high a speed. That can be confused with slipping when it's really just a late up-shift, but it can also cause shifting "runaway" where the engine speeds up momentarily because the clutch pack takes too long to fully engage.