Jailbreak: custom software on stock firmware. This is not Android root.
How-to
How to
Software jailbreak chosen by firmware version per the kindlemodding.org jailbreak wizard: WinterBreak2 (5.6.1.1-5.16.3, also 5.16.5) or WinterBreak (up to 5.18.0.2, device registered); SpiderCat (5.16.3-5.19.5); Nosebleed (5.16.4-5.18.6); Sanctuary (5.16.4-5.18.3, not 5.16.5); Vera (5.17.1-5.20.1.0.2); SpringBreak (5.18.1-5.19.2.0.1, registered); AdBreak (5.18.1-5.18.5.0.1, registered with ads). Then install KUAL (Booklet via MRPI) and KOReader. Firmware newer than 5.20.1.0.2 has no public jailbreak.
Follow the specialist sources linked on this page. If this path is a jailbreak, unlock, or flash, the specialist wiki is the how-to — we do not copy those steps here.
Notes
Firmware-dependent: check Settings > Device Info for the firmware version before choosing a method; do not update firmware first.