Mr Cricket... given that Trott is a middle order player and Carberry is an opener why do you have Trott opening and Carberry at 4?
I think that given his record, whether or not you rate him or not, Cook has to play in the test side for the time being. Also going with the 5 batsman, Prior and 5 bowlers will leave the team likely for at least one collapse a series - which is painful.
Personally I would have a test team similar to the one we have - other than I would have onions in the team and put sidebottom out to pasture. If we could find an out and out quick who could bowl a length then we would have a pretty strong team. Given that we don't have a specialist 3, I put Carberry in, drop Bell and shunt the others down... note the change in batting order, Pietersen is better at 5 than 4 and is not suited to batting at 3. Plus frequently, opening bowlers hate bowling to left handers so having 3 at the top of the order works for me
Cook, Strauss, Carberry (or Bell), Trott, Pietersen, Collingwood, Prior, Broad, Swann, Andersen, Onions/mythical quick bowler
the One day and 2020 stuff has been so hit an miss so far to try and predict a team is almost impossible. But I think you have made a pretty good selection