Mandy,
If the Adenium is going dormant, it would not necessarily have a soft caudex.
I would take it out of it's pot and clean off the roots. Then post a photo for others to see. This would let you see if there is anything going on with the roots and allow someone to give you some sound advice.
It will not hurt the Adenium. The leaves do not look good.
There are many that will help you.
Rick

Here is a picture of the roots, I think they look fine but there wasn't much room left in the pot.
Should I move it a larger pot?

The roots look healthy and clear from rot in photo.
What size pot was it in, in comparison to the size of caudex (1/4", 1/2" from edge of pot all around) ?
The soil around roots looks to be moist?
How long have you had this Adenium?

It had an inch or so on each side, although it's roots were starting to come out of the bottom. The soil is fairly dry and I have only had it for about 5 weeks.

Mandy, the root system looks very good. It needs bigger pot. The leaves didn't look good, but let them fall off during winter, as long as the caudex still hard, then you okay. Don't worry too much.
Marie

As my DR's are going dormant I occasionally notice a plant whose caudex is softening a bit. I'll give it a small drink of water and it will firm up and continue going into dormancy if it's healthy. The root system on your plant looks fine. I'd repot, give it a small drink with some B1 if you have it and allow it to continue into dormancy. If you don't have anything containing B1 just use plain water.

i don't know if this helps but once told by adenium grower if leaves a dying from the bottom up its going dormant,if dying from the top down its fungal or pest.
Frank