I note that many are on the search for a fully supported laser printer. After having installed 4 of those HL-5380DN recently (on 11.2 and 11.3) I can report that they are Linux friendly and fully supported. I added an entry to the HCL: Printers list.
Brother printers are one of the most linux friendly I know with hp. I have 4 of them and they worked out of the box (HL-1440, MFC-240c, HL-5250, DCP-531). Really cool.
I’ve had good experiences with several Brother inkjet and laser models over the last 6 years - using a Brother HL-2150N printer at my current workplace office.