Reading this thread I glean that the airside tunnel connecting T4-T5 has been operational since the latter part of 2014.
Yet the LAX web site is strangely schtum about the T5-T4 tunnel. The main "Airline location" map doesn't show it and the terminal transfer instructions somehow fail to mention T4 completely.

I find it quite incredible that LAX can't be bothered to provide pax with up to date information on their web site.
What one would do without FT I do not know...