The Arduino will show up under the yellow "?" first. I connect the Arduino to the computer, then boot the computer. The first time through, it gave me the "New hardware found", but I did not know where the driver was, so it ended up under the "?" in the device manager.
When I finally got it there, I right-clicked on it, and selected "Properties". It showed no driver. I think I selected "Install driver" or the like, and when it asked where it was, I pointed it at the "drivers" folder in the Arduino folder (where you downloaded it).
When I went back to the device manager, it was under "Ports" as COM5.
If you are certain that the USBasp is your Arduino device, try right clicking on that and removing it. Then reboot the computer.
Or if you are feeling lucky, right click on that entry, select "Properties", and "Install driver", or reinstall driver if it has picked up one. Aim at the drivers folder when it asks.