If support number 1 is the anchor, and 2 through 5 are progressively farther away...

Typically, we would model 1 as an anchor, 2 through 5 as +Y, and 3 through 5 as possessing a guide.

Different users have different practices, but my world would say 2 through 5 have a friction value on the +Y and 3 through 5 will have a gap of 0.125 inches.

I would not expect CAESAR to report moments on any supports except for the anchor.

As for real-world effects...
1. The anchor definitely possesses moments in the real world.
2. The guides - particularly at 3 - might possess moments in the real world. If the pipe from the anchor to the first bend grows 0.125" or more, I'll need to see rotation of almost 5 degreees in the Y axis at the first guide before both guides are contacted simultaneously, which is the only case I would consider non-negligible moment to apply. I'll note that if there is no displacement from the anchor to the first bend, you'd only need to see around 2.5 degrees of rotation in the Y axis to contact both guides at once.

So why no moments on the +Y supports? If the pipe is sitting on a beam, as soon as the pipe pitches forwards or backwards, the pipe is acting as though it's pinned on either the near side or the far side of the beam. For there to be moment - as seen by the pipe - it needs to be more than a pinned condition. But I will note that if you have a hold-down, clamp, etc, you could definitely see a moment and model accordingly.