Quagmire,

Yes; 5 years is for those who are otherwise in non-immigrant visa such as F1. After being here in the US for 5 years, you can treat yourself as resident for tax purpose. However, if you transfer your visa to H1, then your residency count starts from day 1. In that case, there is a first year election rule. Anyone interested can go through publication 519 and determine how they should file their tax return.

As far as my understanding about your visa status being permanent resident, you can get upto $2500 (non-refundable - only reduces your tax liability) Hope Credit (or American Opportunity Credit - named just for this year) for the qualified tuition, fees and course materials. However, how much you can deduct depends upon your income and how much tax you owe and things. 40% of the credit is refundable (you get tax refund even if you do not owe tax). You can certainly get credit for the tuition you paid but I can not tell you how much you get without looking at your other details.