Slimline question? Watts?

Psu of the hp ? capacity ?
The maximum tdp of the card is 71W, if you have a psu with 300W, you might get by.
Otherwise i'd get the 5450 from amd which has a 19W maximum tdp.
Both fits slim cases, since they're low profile.

Where do I check for the psu?

Open the case, there's a sticker on it with the information.

The HP Slimline PC has a 160w PSU.

http://h20000.www2.hp.com/bizsupport/TechSupport/Docume...

That makes it extremely difficult to recommend any graphic card unless you can replace the 160w PSU with a decent quality higher wattage PSU first.... if it is at all possible. Some slmline PCS use non-standard size PSUs.

As long as it has a pcie slot 16x, the 5450 doesn't need auxiliary power, and the maximum tdp is of mere 19W, it will do, i guess.

Why do you want to add a graphics card? If it's simply to get more video output options, then you might be on the right track. If it's to improve gaming performance, you might be disappointed with the minimal gain any card of this type will give.

If you're not computer savvy and you want something that's just going to work, you might want to reconsider this. If you're willing to experiment a bit and have the time to troubleshoot any problems that might occur, go for the 5450.