Circles with centers of $(2,2)$ and $(17,10)$ are both tangent to the $x$-axis.

See the graph here  : https://www.desmos.com/calculator/tnnfqay4wv

The  distance  between the  centers  =  [ (17 -2)^2 + ( 10 -2)^2  ]  = [ 15^2 + 8^2]  = sqrt [ 289]  =  17

So....the  closest  distance  between the  circles  =

17 - radii of both  circles  =

17 - 2 -10  =   

5  units

Here is a formula from essaydune.com to solve this type of problems: C₁C₂ – r₁ – r₂

C₁C₂ is the distance between the centres of the circles

r₁  r₂ are the circles radii