cron seems to be set up correctly but doesn't work

Question

I read this post and checked everything, it still doesn't work. I'm trying to set a new wallpaper every few minutes:

• crontab -e, then line before empty last line */5 * * * * /home/me/.bin/ranbg
• the script in /home/me/.bin has the following

    #!/bin/bash
    DISPLAY=:0
    f=$(ls -d /home/me/.bin/mutables/bg/* | shuf -n1)
    feh --bg-max $f
    /home/me/.fehbg

That last line isn't actually necessary because the script just has the exact same as the second last line. I could have forbidden the creation of it by adding --no-fehbg to the call of feh.

I think:

• The ranbg script has ogu=777 so it shouldn't be because of rights.
• The background is set by the call to feh so it shouldn't be because of a missing DISPLAY, so the DISPLAY=:0 in the script is cosmetics