you are not going to run out of the fan out capabilities of the mcu.
Yes you are, after about 20 inputs you start running out of speed.
you guessed it - at some point around the 35th shifter,
Understandable.
The way you do it is to take the clock and put it into one inverter. Then put that output into the inputs of all the other 5 buffers. You can then take each of the outputs to a group (20 Max) of shift registers.