[ggilman]

What's the best possible scenario for a line out with the iPhone 5s or iPod 5?
 
Also, what amp would you suggest to fit between the iPhone and Sennheiser HD 598's?

 

[KT66]

You can't get an anologue line out from the 5 - digital only
see FIIO E18. That may be your best best, or the AK10

 

[JoshuaA]

Only the CCK cable has the USB controller for DAC.
(Pic courtesy of ExpatinJapan)

 

[JoshuaA]

Do you have 598's? They're open and not very private (when in public, library, etc).
Best to use those Senns at home with your computer+better sound card or DAC/amp... unless you wanted a semi-portable solution around your house.