Sorry I did not see this earlier. I always love to talk about the T5 and setups. Coldshot is dead on with his recommendations. I use Elixir 12's with a wound G, which gives you a full body electric tone and good acoustic tone. Remember though, the T5 is a different animal. It is not an 810 or a Les Paul, it is a T5 and good "T5 tone" can easily be found once you get over trying to use the T5 to mimic other guitars. I also have SansAmp modelers that work very well. For simple pedal and effects, after trying all the DigiTech, Line 6, Boss and other multi-effects, I have found that the Boss ME70 pedal works best for me. The "clean" setting is a great match to the T5 and the effects board works like pedals, so no menus to get through for your settings. The ME70 also has a built in looper that is fun to play. One other thing you may want to do, that I find works successfully with the T5 as well as even my acoustic Taylors, is to use a full range PA cab as an extension speaker to a clean guitar amp. I use small amps like the Roland Cube 60/Cube 80 or even my MesaBoogie subway rocket and use a PA cab as an extension cab. For the T5 that works very well. Since the Taylor expression system uses a magnetic humbucker under the fretboard, it works well with my other Taylors (914ce, 814ce cocobolo, etc.). Coldshot is right in recommending experimenting. Running through a guitar amp will not get you the same full range tone since guitar amps are voiced in the midrange for electric guitars, but you may be amazed at the fullness of your tone. Some acoustic guitarists use electric amps when they use mag pickups like a Sunrise. Fun stuff and remember if it sounds good to you, it is good. I also use a Fishman SoloAmp and a Roland AC90, along with powered QSC K8 cabs.
Have fun with your T5.