Can you run Mass Effect 2 on an Acer Aspire 5720 laptop

I think you can, but make sure that you have enough RAM installed. My acer aspire 5720 laptop only supports up to 4 gb according to the motherboard.
My video card is the Intel chipset family 384MB. Regarding the system requirments for the game it says that you need at least: 1GB RAM for windows xp or if you are using Vista or Windows 7 you need at least 2 GB. Windows 7 may consume the video and Ram and leave nothing for you game. So i recomend switching or downgrading to Windows Xp, and running it on that OS instead of vista and windows 7.

It should work fairly well on Windows xp, but you might have to configure the game to use less resources or disable some lighting, shadows, texture options, colour adjustments etc.....