It's about a 10 minute bus ride to/from the Eagle's Nest to T-4 if things are not going perfectly but not in full meltdown. It's about the same for T-5 with the construction work around the bus gate. Depending on how busy things are at the Eagle's Nest and the mix of T-4 and T-5 busses will determine just how much time between busses.

I'm usually solo (SWMBO doesn't add too much extra time @ LAX) and usually head out of the T-4 club about 30-45 minutes before boarding and just cool my heels at the Eagle's Nest club.