We've had similar discussions here before. If she is as skeptical/reluctant as you say you probably don't have her attention that long. 5 song is probably about right.
When picking them, you should keep in mind what kind of music she typically likes and target at least some of the disc to that.
For example, i've met blues players who considered the Dead messy and incoherent. A good Mr Charlie, Same Thing, Deep Elem, Smokestack Lightning, Big Boss Man, or possibly even Minglewood could really turn their opinion around.
Some younger people have the image that the Dead's music is all spaced out and hard to get into. For one of them, something like Dark Star or Stella Blue would be a bad choice. A song that kicks some ass right of the bat like Shakedown Street, Eyes of the World, or China > Rider would be better.
A lot of people I know shun anything remotely country. I certainly wouldn't try to turn them on with El Paso, My and My Uncle, Tennessee Jed or Brown Eyed Woman.
Not sure what you're friend is into but I hope you see what I'm getting at. Few bands are as diverse as the boys, I'm sure you can find something that does the trick!
