If you build the AB1 type sub, note that a second order high pass filter feeding the satellite is incorporated into the crossover. This is necessary, in my opinion, as if run full range, the LS3/5A has a substantial resonant hump around 100 Hz to compensate for lack of extension (6 dB down by 60 Hz) and this makes mating with any sub difficult.
I know; I've tried blending a pair of nice Hsu's with the Harbeth HLP3s (which are like an upscale LS3/5A in my book) and after a year of trying never came even close to success—but I was letting the Harbeths run full range. This was 25 years ago and both time and money were too tight to allow experimentaion, but I learned that trying for success without high passing them is a waste of time—unless you like sloppy, boomy bass, and some seem to, I've noticed.