The YN-560-TX can only control the power remotely on a YN-560III or YN-560IV. Using it with a YN-565EX will only work if the YN-565EX is on an RF-602 Rx unit, or RF-603, RF-603II, or RF-605 transceiver, and the only control it can offer is firing the flash in sync. (With the RF-605, however, you can also use groups control to turning firing on/off for that specific flash).
The YN-622C transceiver is probably the best companion for the YN-568EX if you want to take advantage of the iTTL, FP flash, and remote power control capabilities of the YN-565EX.
To remotely control a YN-565EX over radio with TTL/FP capability with YN triggers, you'd need a YN-622N transceiver to act as a receiver, and either a second YN-622N or YN-622N-TX to act as the on-camera transmitter unit. The YN-622N-TX dedicated transmitter is much easier to use than a YN-622N transceiver because it has an LCD display to show the flash's settings, while the transceiver only has a few LEDs to indicate channel, group, and power settings.
The YN-565EX (and Mk II) have CLS slave capability, so you don't have to use radio triggers, if your camera body has a built-in CLS commander in the pop-up flash. They also have two "dumb" optical slave modes (S1/S2) which can act like Nikon's SU-4 mode to be set off by any pop-up flash, without using CLS.