The three lights blink simultaneously $ t $ seconds after the start of the dance if and only if $ t $ is a common multiple of 2, 3, and 5. Recall the common multiples of a set of integers are precisely the multiples of the least common multiple. Since 2, 3, and 5 are relatively prime, their least common multiple is $ 2\cdot 3\cdot 5 = 30 $. Thus the light blinks $ t $ seconds after the beginning of the song for $ t=0,1,2,\ldots,14 $, and after 14 thirty-second periods, the song ends. Thus the lights blink in unison a total of $ \boxed{15} $ times.