@spiritofradio - Wasn't really suggesting anything, but I know it's going to be a lot of weight when you get up to a 5x5. What's the largest Kallax you've used to date? And did you fill it? I think I would be concerned about filling the shelves completely, unless you've done it successfully before.
When I built my 4x2, I glued and screwed it for a bit more confidence. It feels very solid. Instead of the back brace like you use, I cut a 2x4 to the length of each shelf and glue in into the back edge of the shelf (standing on edge). The 1.5" depth of the 2x4 makes a perfect backstop for the LPs, leaving the front edge on the LP sticking out the front about 1/2" making it easier to pull the records out when they are stuffed tightly into the shelves.
Good luck with everything. Send us a pic when it's up and loaded.