I think it's much better to go with the 4.0.4 version from the 5113. Everything is butter smooth and works fine. It has some added features and apps (including a 50GB gift for DropBox).
I used Odin to flash the P5113UEBLH1 4.0.4 ROM from sammobile. At first it was stuck on Samsung logo (probably because I had CM 10 and AOKP before), but I went to recovery and did a wipe data/factory reset and loaded fine after that. Then I rooted successfully using this guide.