howManyToFind = 10;
Clear[x, y, z];
conditions = 6 <= x <= 7 && 9 <= y <= 11 && 5 <= z <= 8;
equation = 1.3 == Sqrt[ (6.64730 - x)^2 + (10.17180 - y)^2 + (5.66580 - z)^2];
r = FindInstance[equation && conditions, {x, y, z}, howManyToFind]
gives
{{x -> 6.05293, y -> 9.01563, z -> 5.6658}, {x -> 6.05184, y -> 9.22727,
z -> 5.}, {x -> 6.07746, y -> 9.10928, z -> 6.15194}, {x -> 6.05875,
y -> 10.7719, z -> 6.65749}, {x -> 6.26417, y -> 11.,
z -> 6.5917}, {x -> 6.08437, y -> 9.35088, z -> 6.50198}, {x -> 6.04922,
y -> 9.22892, z -> 6.3316}, {x -> 6.66179, y -> 9.05533,
z -> 5.}, {x -> 6.05934, y -> 9.22258, z -> 6.3316}, {x -> 6., y -> 9.38983,
z -> 6.47791}}