I read somewhere that most schools accept a test result that is two years old. Some schools even allow a four year old result. When a new version of the test comes out that doesn't mean all schools suddenly change their requirements. But they will eventually... I agree that your best bet is to talk to someone at the nursing school and hear their opinion on it.
You can find a review of the ATI Teas V Study Guide at: http://www.teastest.org/study-manual-for-the-teas-version-v-review/ It is supposed to be very good and on Amazon it is sometimes sold out!
According to the reviews the McGraw-Hill book is helpful for science but does not cover everything. Especially for earth science you need to find other sources. I am still looking around ;-)