If f(1) = 5, then you can find your answer by substituting 1 in for x in all of the options to figure out which one gives you 5 as a result.
A: 3(1)^2 + 14(1) + 8 = 25 ≠ 5 Nope
B: 3(1)^2 - 14(1) - 8 = -19 ≠ 5 Nope
C: 3(1)^2 + 10(1) - 8 = 5 Yup
D: 3(1)^2 - 10(1) - 8 = -15 Nope
Only C fits f(1) = 5.