Do you use plain docker like in the example?
Doc Example Docker
docker run \
--name openhab \
--net=host \
-v /etc/localtime:/etc/localtime:ro \
-v /etc/timezone:/etc/timezone:ro \
-v openhab_addons:/openhab/addons \
-v openhab_conf:/openhab/conf \
-v openhab_userdata:/openhab/userdata \
-e "EXTRA_JAVA_OPTS=-Duser.timezone=Europe/Berlin" \
-d \
--restart=always \
openhab/openhab:2.5.0
I also use docker and made a post about my update experience.
And YES @vzorglub is absolutely right, do a backup first