normaly are screen blank not same display physical off. This Tool let hdmi or touchscreen after timeout go power off.
install tvservice (hdmi support) and xscreensaver
Add line to autostart from LXDE (~/.config/lxsession/LXDE-pi/autostart) if you want your touchscreen after 5 seconds off:
~/bin/xscreensaver-displayhelper 5 touch&
Display off after # Seconds
xscreensaver-displayhelper [delay in s]
Display Off after # Seconds only Touchscreen or HDMI
xscreensaver-displayhelper [delay in s] [touch|hdmi]
status of display (on|off)
xscreensaver-displayhelper -s, --status "
Touchscreen/Hdmi off
xscreensaver-displayhelper -f, --off
Touchsceen/Hdmi on
xscreensaver-displayhelper -o, --on
Help Text
xscreensaver-displayhelper -h, --help
Based on https://github.com/ramses0/xscreensaver-pi-hdmi/ and https://www.raspberrypi.org/forums/viewtopic.php?t=56944&p=429723 I add Support for 7" Touchscreen and few flags