Your Trek is a very nice bike and more than capable for a 5 mile commute, but it will pick up the grime and wear out bits quicker.
It could be more cost effective to pick up a second bike for less than £300 and keep your best bike for those all day rides. With a dedicated commute bike, you can load it with mudguards, heavier tyres, luggage racks etc and you can be less strict in the cleaning routine. And at the weekend, the best bike is sparkling clean and ready to go.
Does worry me that you are taking the bike into the shop for a flat tyre. You should be self sufficient with fixing punctures.
Enjoy your commutes, it's a great way of keeping fit.