Hello,
Beware that exports is not consistent unless you open your database in restrict mode.
An import of 5gb will take forever... (beware the size of the redo logs during import to avoid too many log switches).
Do you have your own database instance on the new server ? If yes, then do as you would for a full cold backup : stop the database, and copy the datafiles, control files, redo logs, parameter file to the new server.
Then edit the parameter file to reflect the new path to the control files (and path to the archived redo logs if needed). Open mount your database and specify the new path to all the datafiles and redo logs with "alter database rename file '/myfile.dbf' to '/newfolder/myfile.dbf'" instructions.
If you share your instance with other users, then you are doomed to use exp/imp.