JWS/JWT Header X5C

Hello All, 

I'm trying to sign some custom JWT with x.509 certs but running into a problem with the signed JWT containing some information I need in the JOSE header.

Is there a way to get the "X5C:[]" header included in the signed JTW? IS this as easy as setting something like the following

Set JOSE("x5c") = "public key"

Thanks

John