The second number in the given number-pairs is obtained by performing certain mathematical operation(s) on the first number. The same operation(s) is/are followed in all the number-pairs, except one. Find that odd number-pair.

Look for a simple linear operation of the form $$\alpha\,n+\beta$$ that takes the first number $$n$$ to the second number.

Try $$n \times 13$$ because 13 is a convenient trial factor (it divides numbers near 90, 100, 78 seen in the options). After that multiply-add test, subtracting 2 brings the products exactly to the second numbers in three of the four pairs:

Case A:
  $$7 \times 13 = 91$$
  $$91-2 = 89$$ ✅ matches the second number.

Case B:
  $$8 \times 13 = 104$$
  $$104-2 = 102$$ ✅ matches.

Case D:
  $$6 \times 13 = 78$$
  $$78-2 = 76$$ ✅ matches.

Case C:
  $$5 \times 13 = 65$$
  $$65-2 = 63$$ ❌ does NOT match the given second number 60.

Thus the common rule for the correct pairs is
  Second number = $$(\text{first number}) \times 13 - 2$$.

The only pair that violates this rule is (5, 60).

Hence the odd number-pair is:
Option C which is: (5, 60)