It'll probably be sturdy enough, although I expect you might get some sway in a stiff breeze. That'll probably set off your motion alerts unnecessarily in really gusty conditions, but if you know in advance and haven't installed the pole yet you can take a bit extra care to avoid shaking/swaying. Some higher end Hiks have anti-shake compensation in the firmware that you can turn on for cams stuck on actual poles (long pipes). Not sure how far down the camera line that feature goes (don't remember seeing it in the cheapo 3345-I firmware but it's in the 4X26 Darkfighter firmware), but I bet it's more useful on cams mounted on long pipes than short stiff poles like the one in your pic so I wouldn't bother popping big bucks just for that feature.
If it's staring back at the house you might consider lawn floodlights, say 1/3 of the way back to the house from the camera pointed at the house instead of house-mounted floods for extra light. They don't give good results staring into floodlights. Also, the cam should preferably be mounted a bit over the roof level of any cars routinely parked in the driveway or you won't see much on the far side of the cars. 5' might be cutting it close to being too low if you depend on the view behind the parked vehicle. That's nothing that a cam mounted on the house pointed out won't solve, but then you have to decide which way to point your floodlights- help the house cam, hurt the lamp cam.
It might require some experimentation. Floods mounted high on the house out of direct view of the lamp cam wouldn't blind the lamp cam but would throw some shade on any detail it might see. Best solution is cams on the house pointed out with additional lights pointed out. Lamp cam is a good idea but I'd point a camoflaged lampcam outwards in addition to house-mounted cams unless there's part of the cam-on-the-lamp scenario that I'm not seeing from this side of the screen.