The best way to get fast cxp ranks now in 5.0 SWTOR:
1. Farm ranked warzone/galactic starfighter
For 1 ranked lose i get 795 cxp, for win 900+
In the meantime waiting for pop up do planetary missions
(ctrl+g->planetary missions). For example if you choose coruscant, you have to do only 4 easy heroics 20 cxp each+ you will get 450 cxp for completing the mission.
With this system i can make 5-15 levels daily, depending on time spent on game.
2. Remember to check daily bonus under ctrl+G. Bonus=20% to mentioned activity.
For example:
If you do a lot of operations dont use the cxp items from bosses yet. Wait when there will be operations bonus day. Wait for our dark or light side win to get additional 15% bonus, open your comand boost and then use all cxp items from ops. (total of 55% more cxp this way)
3. Kill 1st boss of blood hunt solo mode for 100 cxp
2 min=100 cxp
For now those are the most efficient way of gathering cxp.