Hello,
I am using TPS54560 for 5V generation on my board and pulling its EN pin with its own output as shown below with a series diode. If diode is not present, this converter never turns on, hence used a diode.
And also i have many converters on same board for 15V, 24V, 19V etc.. generation on same board with TPS54560 and pulling EN pins of all these converters with 5V generated from above said converter. I hope this shall be OK.
Thanks & Regards
Ganapathi