*A lounge is at TBIT and 5 hours is plenty so don't sweat it. You can check in at *A lounge or you can go to the gate and check in. Gate should be staffed starting around 2 hours prior to departure. There is also self-check in kiosk at TBIT air side but I don't recall if SQ participates in that program.

From T7 to T6 is a simple walk from the gate level concourse. From T6 to T5, you need to go downstairs to the basement level and take the tunnel. And tunnel again from T5 to T4. When you reach T4, you need to make a sharp turn and find the stairs that go up to departure level. Once you get up there, turn right and head towards gate 41 and you will see the connector to TBIT. Take the escalator up to the connector and you will see signs to airline lounges when you reach TBIT. This is a 20 min leisurely stroll or you can do it in about 15 min sprint.