i need to know if this is compatible

Your computer is not a good gaming model. There's a lot more to consider than just a video card--cpu speed, power supply, memory, cooling, etc . And all that is expensive and can be found in expensive high end models. That video card you ask about requires a 400w power supply, which is probably more than you have. Save your money. The 4350 is a decent video card for your model computer and that slim case limits what you can replace or add.

That particular video card is so new, it isn't even listed on gpureview.com.  While the card will probably fit in your system, the greater concern would be your power supply.  I believe you only have a 250W unit, and the specs on the HD-5570 recommend at least a 400W power supply.  Now granted, sometimes they overstate the power supply requirements for video cards, but trying to run a 400W recommended card on a 250W power supply may not work.  (I did run a HD-4670 for over a year on a Dell 300W PSU without any problems, but that is a 300W PSU)  That is the main drawback to the slim form cases, is that they aren't as upgradeable as a mini tower or mid tower.  I also don't think it is as cheap and easy to upgrade the power supply in one of those cases.  Let's be honest, the slim cases are designed to be simple email and word processing systems, not game playing monsters.  Most of the really powerful cards are too large to fit, and demand too much power, and generate too much heat to be used in those type of systems.

IMO, the best option for you would probably be a low profile HD-4650 card, if you can find an affordable one.  They suggest a 300W power supply, but it might be possible to run one on your existing system.  It would also about double the performance of your existing card.

My friend told me Geforce is good for games. would one like this be compatible with my computer? 

http://www.newegg.com/Product/Product.aspx?Item=N82E16814187083

My friend told me Geforce is good for games. would one like this be compatible with my computer?    http://www.newegg.com/Product/Product.aspx?Item=N82E16814187083

You seem not to pay the least bit of attention to the advice that was given.

If you wanted a gaming system, why on earth did you buy an Inspiron 537s :emotion-18:

Whatever... read what 2ndtimer has said, before asking any more upgrade questions :emotion-55: