Lets look at the coils. Both the 11" and the 5" DD are speciality coils, additional tools, which allow your detector to perform better in different site conditions. I haven't posted much about the 5" coil yet because I haven't got to hunt much in the last 60 days (that is soon to change though) and I wanted to put a side by side comparison of all three (4 if you count the little 4" BH coil) together. But I do have a little time on it.
This is what I do know about the 5" coil: It will drop your FE ground readings. It will hunt in very high to extreme trash. It will enhance the micro jewelry and prospecting ability of the F5 (I need to post some pictures) So if I'm hunting a site that has extreme trash, I'm going to be running the 5" coil. If I have located a good area for micro jewerly (thin chains, earring backs and posts, etc), then I'm going to be running the 5" coil.
However, If I'm cherry picking in that 7' feet alongside the park sidewalk that contains the usual amount of foil, tabs and bottle caps, I'm going to run the 11" coil because the extra ground coverage combined with the additional target separation makes it the better coil for the site. If I'm cruising outside the hot spots at the park or atheletic fields, I'm going to be using the 11" coil because the ground coverage is more important and I'll get more and better finds with the 11" coil.
I guess I should also mention the little 4" BH coil. It will air test 5" to 6" but has trouble in the ground once you add minerals just because it is not tuned to work specifically with the F5. However...it is a little laser (and I do mean laser!). The bad part of this is that the target area of the coil is about the size of a quarter. So imaging sweeping a coil the size of a quarter on the end of your rod.

I much prefer the 5"DD coil over the 4"BH coil because of the better depth and ground coverage of the DD, but again there are sites where this coil might be the better choice.
Its how and where you hunt that makes one coil better than the other. Just review the sites you normally seek out and hunt the most and let them drive your assessory coil selection.
HH
Mike