Plaster to Drywall Door Jambs
 

Do they make a door jamb that is 5 3/4" wide? If not, what can I do to replace an existing jamb with a new one?

Thanks

That's a good thick wall, There are door jamb sets available by special order from most suppliers. They are made for older plaster and 2x6 framed walls.
I usually just make my own. A tablesaw makes this a much better looking job.
If you do not have access to a tablesaw, an edge guide on a circular saw will do a nice job. Be careful, keep the saw moving and you will reduce the chance of burns from the side of the blade.
a 1x6 is only 5 1/2" wide. you will have to use 1x8s. All said and done, it may be cheaper to special order them or have someone else make them for you.

You can also add a filler to a narrow jamb to make it wider. The filler has to go on opposite of the hinges for the door to have a full range of swing.

The fillers are the most common, but not extremely attractive.