If you had N4 that would be a different story, but even then N4 to N3 in 5 months (for an average learner) might prove difficult to achieve. Sure you're welcome to try, but the test for N3 is not a walk in the park like the tests for N5/N4 (go check out some old tests online). So I'd say go for N4.
Edited: 2016-01-30, 4:39 pm