Is this correct?
There are five people going with we members.

Us. Try the sentence without the word members, and it becomes obvious.
 "There are five people going with we" really sounds strange. "There
are five people going with us" sounds infinitely better.

The   form of a word changes as they function as subject or object.
The subject will be we; the object will be us. In this case, the five
people are subjects; the members are objective.

A good source of grammar information is ELEMENTS OF STYLE by Strunk &
White. If out of print, it will be available used.

irlandes-ga is 100% correct, drop the objective and see which subject works best.

another example that may be easier to understand the way it works would be to take

"Bob went to the mall with Jill and I."

Break it down and if both parts make sense then the whole does as
well.  "Bob went to the mall with Jill" works but "Bob went to the
mall with I" does not, so you would use "me" instead.

The sentence is incorrect since "we" is a pronuoun and it cannot use
as a modifier of the noun "members". The correct answer should be
"our" which is a possesive pronoun and can therefore be used to modify
the noun "members".

The only way this sentece is correct is if there is an organization
whose initials are "we", and in that case the correct spelling should
be "WE" or "W.E." members.