I finally did it...I registered for my first 5K!!!!

 I love running outside and I think your trainer is right try out different terrain. Can you do the 5k course for practice runs?
Like someone mentioned before wear a lightweight jacket you can tie around you or one you can drop and come back for.....keeping in mind you might never see it again.
I always trained with music but I have found some of the larger races frown upon music so it is up to you. I personally wished I never did start w music. 
Good luck it is addicting. I can honestly say I never ran a 5k I always chickened out but last year I did a half marathon and it was so much fun! Your gonna love getting caught up in the moment!
Congrats and goods luck!