u can rebattle trainers each week.. and u can gym leaders over and over, cause thats the real progress. the elite 4 can be u rebattle after a 24 hour wait.
soo to answer ur question, no u cannot go though the whole game with a level 5, not if u wanne beat the game.. u can battle normal trainers lose and pass them after.. but u wont get xp.. guess thats it :)