The BG5000 is a bit big for 11' rods and also a bit on the heavy side.
I will rather pair it with a BG4000.
It must be taken into account that the Daiwa BG series (BG, BG Magseal, BG MQ's) are all about the same size, but they are bigger than the same number sizes in other brnads, ie. Shimano 4000 is way smaller than the BG4000.
I use a regular size Daiwa Regal 4000 which pairs nicely with 10'6 and 10' rods, is more comparible to the BG3000/35000.
The BG4000 should really fit the 11' like a glove.