How do I add music to my iPhone without deleting previous songs?

So my iPhone 5 has always been synced with my sister's computer and her music library. My itunes library on my PC only has very few songs that I now want to put on my phone. I have read tutroials that tell me to go under the 'Summary' tab and select 'manually manage music and videos', then 'apply'

But when I do a pop up warning come up saying

Is there a way around erasing the current content?

Both iPhone and iTunes are up to date with software.