At any instant, how many complete sine waves will be visible to a viewer looking at your system ?
In the video you linked to, it appears to be about three quarters of a sine wave and the frequency looks like about 0.2Hz
Anyway if, as suggested in post #2, concentrate on getting one servo working correctly, so that you can specify the angle say between 0 and 180 degrees, the rest is very easy because because the position of each servo is related to the position of the first one. And the position of the first one is related to time.
Say at the start of a sequence, servo 1 is at 90 degree, servo 2 must be at 180 degrees, servo 3 must be at 90 degrees, servo 4 at 0 degrees, servo 5 at 90 degrees etc. etc. You'll want to regulate the speed at which this cycle repeats for a reasonable visual effect.
This relationship depends on the granularity of your display, that is what proportion of a sine wave should be visible at any instant. You'll obviously want it finer than the example above, and for the intermediate values, you have to use a sine table.