I don't know if there is a command to indicate what driver is being used by the X11 system. I also don't have a functional debian system at the moment but running
sudo grep driver /var/log/Xorg.0.log
on my Fedora 22 laptop gives:
[ 40.931] X.Org XInput driver : 21.1
[ 44.288] (==) Matched intel as autoconfigured driver 0
[ 44.288] (==) Matched intel as autoconfigured driver 1
[ 44.288] (==) Matched modesetting as autoconfigured driver 2
[ 44.288] (==) Matched fbdev as autoconfigured driver 3
[ 44.288] (==) Matched vesa as autoconfigured driver 4
[ 44.288] (==) Assigned the driver to the xf86ConfigLayout
[ 44.288] (II) Loading /usr/lib64/xorg/modules/drivers/intel_drv.so
[ 44.642] (II) Loading /usr/lib64/xorg/modules/drivers/modesetting_drv.so
[ 53.891] (II) Loading /usr/lib64/xorg/modules/drivers/fbdev_drv.so
[ 54.058] (II) Loading /usr/lib64/xorg/modules/drivers/vesa_drv.so
[ 54.084] (II) FBDEV: driver for framebuffer: fbdev
[ 54.084] (II) VESA: driver for VESA chipsets: vesa
[ 54.096] (II) intel(0): Using Kernel Mode Setting driver: i915, version 1.6.0 20151010
[ 54.166] (II) intel(0): [XvMC] xvmc_vld driver initialized.
[ 54.166] (II) intel(0): [DRI2] DRI driver: i965
[ 54.166] (II) intel(0): [DRI2] VDPAU driver: va_gl
So it looks like I'm using (on my laptop, not the G5) either the intel driver, the fbdev driver, or the vesa driver.
sudo grep -i fbdev /var/log/Xorg.0.log
[ 44.288] (==) Matched fbdev as autoconfigured driver 3
[ 53.891] (II) LoadModule: "fbdev"
[ 53.891] (II) Loading /usr/lib64/xorg/modules/drivers/fbdev_drv.so
[ 54.058] (II) Module fbdev: vendor="X.Org Foundation"
[ 54.084] (II) FBDEV: driver for framebuffer: fbdev
[ 54.099] (WW) Falling back to old probe method for fbdev
[ 54.099] (II) Loading sub module "fbdevhw"
[ 54.099] (II) LoadModule: "fbdevhw"
[ 54.099] (II) Loading /usr/lib64/xorg/modules/libfbdevhw.so
[ 54.110] (II) Module fbdevhw: vendor="X.Org Foundation"
[ 54.119] (II) UnloadModule: "fbdev"
[ 54.119] (II) Unloading fbdev
[ 54.119] (II) UnloadSubModule: "fbdevhw"
[ 54.119] (II) Unloading fbdevhw
so it's not using the fbdev driver
sudo grep -i vesa /var/log/Xorg.0.log
[ 44.288] (==) Matched vesa as autoconfigured driver 4
[ 54.058] (II) LoadModule: "vesa"
[ 54.058] (II) Loading /usr/lib64/xorg/modules/drivers/vesa_drv.so
[ 54.084] (II) Module vesa: vendor="X.Org Foundation"
[ 54.084] (II) VESA: driver for VESA chipsets: vesa
[ 54.110] (WW) Falling back to old probe method for vesa
[ 54.119] (II) UnloadModule: "vesa"
[ 54.119] (II) Unloading vesa
so it's not using the vesa driver
Must be using the intel driver (which makes sense since this is an i7 laptop).