A few things to note: the 15" sides are needed because the snare guards on the Super Sensitive protrude, and the drum needs to be placed in the case with the guards facing the corners. Also, it is imperative that the case have padding. Super Sensitives are, well, super sensitive and the slightest jarring will knock them out of adjustment. Ideally the case should be 5.5" tall for Super Sensitives made from 1969 on because the snare guards on those models extend downward, increasing the height of the snare drum. However, the SKB 5 X 15 Square Snare Case has sufficient depth in the top half of the case where it will still secure the snare drum without needing to be fully seated.
Also note that on the product page I linked the photo of the case is incorrect. A round case is depicted - the actual case looks like this:
The case will fit both the pre-1969 Super Sensitives and the ones made from 1969 on. It is a bit pricey, but well worth it in my opinion because it will protect your investment.
If you have a Super Sensitive and are having problems adjusting it check out my entry about Adjusting Ludwig Supersensitive Snare Drums.