is there any advantage to upgrading from light room 3 student teacher edition vs. buying the new version outright?
There is no discounted upgrade path from LR3 Student and Teacher to LR5 Student and Teacher. You must always buy the full Student and Teacher version.
If you mean upgrading from LR3 Educational version to LR5 retail version then whenever you need to re-install the new version, you will always need your Lightroom 3 serial number to verify your upgrade serial number.
Other than that, no difference other than price.
Is it less expensive to upgrade vs. buy outright...did not seem so
Best to quote specifics to make clear decisions.
Lightroom 5 (retail) - Upgrade from LR3 = US$79
Lightroom 5 Student version = US$79