we know that the two circles touch if
C1C2=r1+r2 [Externally]
C1C2=r1−r2 [Internally]
In case they intersect in real points , then
C1C2<r1+r2 and C1C2>r1−r2 ...(1)
C1 = (0 , 0) , C2 = (5 , 0) , r1 = r , r2 = 3
∴ 2 < r and 8 > r i.e. r < 8
Hence the required condition is 2<r<8