From the information you've provided you are way off on either the model of laptop you have or the type of processor you have. Most likely you have a different processor then you think.
Buy from Crucial. They have a system scanner that will determine what type of memory your system uses and they guarantee that it will work. They also offer free shipping and limited life time support.
you haave to check the I agree box in order to run the scanner. It will popup a download file window. Just hit run or open. After a few seconds it will run and start the scan. It takes about 10 to 30 seconds assuming your internet connection is broadband.
I have an Acer Extensa 5420 and went to crucial.com and used their configurator and they were selling a 2 pack 2GB SODIMM PC2 5300 for $44 with free shipping and limited life time warranty.
On Acers support site they say for the Aspire 5220 you need PC2 5300 and that your motherboard chipset is nVidia nForce 630M It also states that your processor is a Mobile AMD Sempron 3500+ 1.8GHz
If it is an Extensa 5220 you need PC2 5300 as well and that you processor is an Intel.
Either you have the wrong model, or the wrong information about what processor you have. Most likely you have the wrong information about what processor you have.