I figured out a pretty easy way to do this

First, create a circle (not a sphere) and tab into edit mode. Press 'A' and 'F' in that order to create a face.

While in edit mode, grab the face, hit 'G', 'X' and press '2' in that order to move it to the right.

Stay in edit mode, press period key, and change it to 3d cursor.

Then, grab your circle, hit 'Shift+D', 'R', 'Z', '60' in that order. Repeat this 5 times to get this:

After you get this add the screw modifier, and it should work

I figured out a pretty easy way to do this

First, create a circle mesh (not a sphere) and ↹ Tab into edit mode. Press A and F in that order to create a face.

While in edit mode, grab the face, hit G, X and press 2 in that order to move it to the right.

Stay in edit mode, press period key, and change it to 3d cursor.

Then, grab your circle, hit ⇧ Shift+D, R, Z, 60 in that order. Repeat this 5 times to get this:

After you get this add the screw modifier, and it should work