My first thought was "Why not check the bags thru" until I remembered the new rules that went into effect Jan 1. Even it it is not technically allowed, you can always ask when you check in. I've had some luck when asking nicely and getting baggage rules "bent" (mostly when I have a 23 hour layover on an international trip and I want the bags checked thru)

The terminals at LAX are laid out as big U -- terminals 1 2 & 3 down one side, the Bradley Terminal (TBIT) at the base and terminals 4,5,6,7 & 8 up the other side. KE is at the TBIT and DL is in Terminal 5.

Without bags (or only hand or rolling luggage) I'd say just walk. It would take 10 minutes if you were slow. If you have more, there is a shuttle bus but the hassle of getting on and off with luggage is probably not worth it. I'd just rent one of the "Smarte Cartes" and wheel your stuff along.