We present NH3 observations of the B5 region in Perseus obtained with the Green Bank Telescope. The map covers a region large enough ( 11'?14') that it contains the entire dense core observed in previous dust continuum surveys. The dense gas traced by NH3(1,1) covers a much larger area than the dust continuum features found in bolometer observations. The velocity dispersion in the central region of the core is small, presenting subsonic non-thermal motions which are independent of scale. However, it is because of the coverage and high sensitivity of the observations that we present the detection, for the first time, of the transition between the coherent core and the dense but more turbulent gas surrounding it. This transition is sharp, increasing the velocity dispersion by a factor of 2 in less than 0.04 pc (the 31'' beam size at the distance of Perseus, 250 pc). The change in velocity dispersion at the transition is #3 km s-1 pc-1. The existence of the transition provides a natural definition of dense core: the region with nearly constant subsonic non-thermal velocity dispersion. From the analysis presented here, we can neither confirm nor rule out a corresponding sharp density transition.