AMD A-10
http://www.bestbuy.com/site/asus-15-6-laptop-amd-a10-series-8gb-memory-1tb-hard-drive-gray/4882013.p?id=1219644187138&skuId=4882013
Better Graphics: http://www.videocardbenchmark.net/compare.php?cmp[]=2899&cmp[]=2908
A10 wins in 3d games like league of legends, but loses on 2d games.
Better CPU: http://www.cpubenchmark.net/compare.php?cmp[]=2451&cmp[]=2440
Because AMD has 4 physical cores vs 2 physical core of the intel i5, i5 wins in single threaded tasks, but A10 wins with multi-threaded tasks.
Cheaper: A-10 = 429.99. i5 = 479.99.
More ram: A-10 = 8gb. i5 = 6gb
More storage: A-10 1000gb. i5 = 750gb.
Here is the tricky part. According to Bestbuy the A-10 only uses a wireless N connection. According to this article: http://smallbusiness.chron.com/can-laptop-computer-n-card-pick-up-g-router-internet-signal-69824.html, wirelles N cards can pick up an A connection and also a G connection.
If I were you, I would pick up the A-10. Test it if it does connect to A/G/N connections, your router/modem must have to ability to switch between those. If it connects to all 3 types of connections good. If it only connects to an N type connection, verify with your school if they have an N type connection. If not, return A-10, best buy is really nice about returns (7-days I think), and buy the i5. If bestbuy asks why you want to return the product, say it did not connect to my modem.
EDIT:
My older A-10 4600M APU with Radeon HD 7660G can run League at maxed settings 80 fps only dropping to 40 fps when in teamfights.
My gaming laptop lenovo y50 when only using the intel graphics card and not using the nvidia graphics, intel i7-4710HQ + intel HD Graphics 4600 can run League at maxed settings 60 fps and drops to unplayable framerate of 15 when in teamfights.