1) On the first computer, make sure Mediashout is closed.
2) Go to the start menu search bar and type %programdata% and press enter. That goes to the C:/ProgramData folder which is hidden.
3) Then go to MediaComplete and then Mediashout 5 and then Song Library
4) Copy the Songs5.mdb file (this is your song library) to a flash drive, etc.
5) Take the file to the new computer
6) Make sure Mediashout is closed on the new computer.
7) Go to the same place (start menu search bar and type %programdata% and press enter and then to MediaComplete and Mediashout 6 then Song Library) and put your Songs5.mdb file into that folder. I would recommend renaming the first one before you do to songs5_original.mdb so you can have that as a backup.
8) Open Mediashout and you're done-- you'll see the songs.
Alternatively, you can even import the database by going to Insert Lyric in Mediashout, then the gear icon, then Add Lyrics, From Files, and browse to the Songs5 file (may need to change file type to see MDB files) and click to import.