How to reach R4 or R5?

Do you mean become an R4 or R5. Or contact the R4/5 of an alliance?

To be an R4 of an alliance the leader needs to promote you to that level. Being an active member in all events will help you. To become R5 (alliance leader) you need to start your own alliance or the leader of your current alliance would need to transfer leadership to you.

You can send any players a message in the Mail screen using the Send Mail option. You can tap on any player in your alliance list to find a mail option. Or tap on a base in the world and select the info option then 'Send Mail' button. You can also check their alliance with the 'Alliance button' and find an option to 'Contact Master' which will let you message the R5 of that players alliance.