Can I use Cat6 cable with Cat5e sockets or a Cat5e patch panel?

It may be physically possible if the termination hardware accepts the conductor size, but the finished channel is then limited by the lower-category component. Cat6 cable does not promote a Cat5e outlet into Cat6.

If you want a Cat6 permanent link, use Cat6-rated connecting hardware throughout and test the completed link to the required Cat6 limit.