Need better graphics card!!!!

You might be able to fit a low profile graphics card into your system but if you do you'll also need to upgrade your power supply which is troublesome because, like the graphics card, you'll need a special, smaller PSU to fit your slimline case.

The card recommended by drtweak requires a minimum of a 400 Watt power supply as noted in the specifications. Your HP slimline has a 220w power supply.

If you're entering the PC gaming culture, it may be best to sell your slimline and put that money towards a custom gaming build.
 
I've put similar card is smillar systems (250 watt range) without issue. I don't think he will have an issue and besides finding a higher wattage PSU for a slim like would be hard to find.

Most name brand PC's come with 300 watts or less. NEVER had an issue tossing in a like a GT620 or anything that doesn't require an extra power connector.

And that card was just an example. there are other cards that require less.