Do not go airside if you can help it. There is no direct airside T5->T4 bus atm. If you can go landside and use the HEX via the LHR central station (you will have to change) or tube via Hatton Cross (again a change is needed) or better still if you havn't got too many bags the free TfL buses 482/490 from stand 7 at T5. Going landside will involve going through immigration though.
See this post for an explanation
https://www.flyertalk.com/forum/30861820-post441.html