How do I backup previously downloaded music to iTunes?

I recently got a new computer. On my old computer I downloaded all of my music to my iPhone 5s and have over 400 songs. On my new computer, I cannot download music to my phone unless I press the "Sync" option in the music tab; however if I do I have to delete all of the music that's already on my phone. Is there anyway I can download the music from my iPhone to my iTunes library?? Thanks in advance