It's a low profile card, should fit. You can tell pretty well by the images, it extends not much past the PCIe connector and the fan barely if at all extends past the mounting bracket.
Yeh, the specific 'slimline' HP pc doesn't
accommodate the card (once I looked at my friend's computer) and therefore, we're exploring other ideas of finding if an internal card can be added from the inside as opposed to the general process of adding to the back of the pc and the biostar graphics card you linked to is a good one and hopefully there's an alternate route but this is secondary project or that is, there's a laptop that's used for friend's main computer and this HP slimline's sort of like the second computer.
Thanks for your input and info.!