Sounds like a full scale Sidewinder missile to me. I've been looking for 5" tubes for that also. 5" ID is the closest I've found, would have to make the couplers though.
the sonoco tubes are 5" I.D. around 5.4 o.d i can get you some exact measurements if you need. Since I am using them as forms it didnt really matter to me. I make the couplers off of foam that I turn on a lathe, seal the foam, layup over it and then remove the foam when it is cured.