1. Format your flash drive or any USB media device for that matter, to EXFAT. you can do this with a number of tools, not gonna hold your hand through that one thou sorry (if you have hands, that is)
  2. Create a series of folders on that flash drive as follows "PS4>UPDATE" IT IS IMPORTANT THAT THE NAMES ARE IN CAPS! ( So that's a folder on the root of the stick named "PS4" and a folder inside the PS4 folder named "UPDATE".)
  3. Download the 5.05 firmware update from https://darksoftware.xyz/PS4/FWlist . You want to download the retail firmware for 5.05. be very very careful not to click 5.50 or any other firmware for that matter, I know you're excited, just take your time.
  4. Once downloaded place the "PS4UPDATE.PUP" file on the USB stick inside the "UPDATE" folder.
  5. Now that the update file is on your USB stick insert the stick into the PS4 and also plug your ps4 controller up via a USB cable to the system. power it up by holding the power button until you hear a beep, once you hear the beep, let go of the power button.
  6. Once the recovery screen boots up select option number 3 "UPDATE FROM SYSTEM SOFTWARE" then "UPDATE FROM USB STORAGE DEVICE" you will then see a screen saying to connect the removable media with the update file, click OK.
  7. The system will now copy the update to internal storage the afterwards update the system firmware. and then you're on 5.05.

Tutorial on updating to PS4 firmware 5.05 from 4.05 or 4.55 by Osama Waheed (Discord)