While it doesn't take away from the magnitude of sending a grand piano-sized suite of instruments and cameras to Pluto, both the planetoid and the NH probe are actually closer to 5 billion km away[0][1].

Pluto does indeed have an aphelion at some 7,311,000,000km (~48 AU), but its eccentric orbit means that its perihelion is about 20 AU closer to the Sun than its aphelion.

  [0]http://spaceprob.es/newhorizons/
  [1]http://pluto.jhuapl.edu/Mission/Where-is-New-Horizons/index.php