A little playing around with plane figures (and/or distance equations) will convince you that this set of points is a sphere centered at
... c = (4b -a)/3 = (25/3, 1, -11/3) . . . . center
with a radius 2/3 of the length ab.
... r = (2/3)√(7² +3² +5²) = (2/3)√83 . . . . radius
Then the equation of this spherical set of points is
... (x -25/3)² +(y -1)² +(z +11/3)² = 332/9