God the Acer website is bad... It maybe me but I am having trouble finding information on their computers... they could learn from HP or Dell...
Anyways I found this, not sure how accurate this is
Aspire E560 (43MR16)
• Intel Core 2 Duo Processor E4300
(1.8GHz, 800MHz FSB, 2MB L2 cache)
• 1GB DDRII RAM
• 160GB SATA HDD
• DVD Super Multi Drive
• ATI Radeon X1550 512MB Hyper Memory PCI XPress
• 9-in-1 Card Reader
• 10/100/1000 Gigabit Ethernet
• Windows Vista Home
• 17” LCD Monitor
Not 100% on this however it is almost certain that you have a PCIE slot in there so yes you can run that videocard.
Open up the case and verify that your Power Supply is at least 400W
It might even work on 300W however the PSU will be peaking a lot during gaming and may eventually go "pifff" so I recommend getting yourself a Thermaltake 430W as they are very reliable and cost effective.http://www.newegg.com/Product/Product.aspx?Item=N82E16817153023&cm_re=430W-_-17-153-023-_-Product