There can be more than one person that writes a song so on my Songs table I have the fields: writer1, writer2, writer3, writer4, writer5.
This is not a good starting point. In addition to Contacts and Songs, you should have a third table - say Credits - to act as a join table between the other two. Each record in the join table signifies a single contribution of one person to one song.
See a basic demo of a join table here: