Someone asked this a couple months ago. It just so happened I was switching planes at LAX the next day so I timed how long it took. I did have to go from Terminal 5 to Terminal 6 and it took under ten minutes from gate to gate. I walked the tunnel, but there are electric carts that would have cut the time considerably.

Do NOT decide to get a hamburger at Ruby's in Terminal 6, though. IME, the LAX outlet is the slowest airport restaurant in the US. Last time, I was standing next to a woman who was flying with her grandchildren. As we were waiting for 15 minutes, she told me she owns several McD franchises in LA. She kept pointing out the reasons the restaurant was so slow. This was my second 15+ minute wait at that place.