No you can't adjust the height when the tv is mounted to the stand but you can adjust the height of the bracket on the back of the tv prior to mounting to stand. No bracket mounting screws are provided so you will need purchase from a hardware store. M6 x 20mm is the size i think. Good stand though.
You fix 2 upright brackets to the back of the TV, then the brackets hook onto the frame, which is then tightened.
If you don't get the height right first time, which we didn't it is really easy to unhook it and reposition the upright brackets. We couldn't believe how simple it was to set up. So unlike most part assembled units.
I can't remember if the screws were already inserted in the back of the TV and we just had to remove them to fix the brackets, or if we used the ones that came out of the TV's original stand. I know that from coming home from work we had it set up in about 30 minutes.
Hope this is helpful.
Ours is set across a corner, but if the back of the distance from the back of the unit, measured as if it was back against the wall, to the back of the TV is 5 inches/13 cms
Hope thismis helpful to you