The controller outputs go to inputs on the 595 chip; no problem here.
I only use DHT22, my understanding is DHT11 can run on 3V3 (use a pullup on output).
Some adventuresome people use 5v outputs connected to 3V3 controller inputs but all bets are off if things will continue to work.
For the 165:
A 5v output through a 1k resistor to schottky diode anode to a 3V3 input with cathode connected to 3V3 can work.
However, 74HC595 AND 74HC165 can run at 3V3.