Well, I'll take a stab at this.

I know when you do a DB restore, the same disk layout (i.e., number of
DBVOLS) is NOT required, been there done that.
I believe the requirement is that the RESTORE TO data base (and recovery
log) must have AT LEAST as much space available as the original, although I
cannot remember where that is documented.

If this is a one-time move, what I would do is use the REDUCE command to
pare the source DB down to 5 GB, then back it up, then restore it to the new
location.  If this is a DR drill, then I think you have a problem, but
congratulations on asking the right questions before it's too late!