The correct answer is $\boxed{\text{C) }5A_{16}}$.
To convert an octal number to hexadecimal, you can use the following table:
| Octal | Hexadecimal |
|—|—|
| 0 | 0 |
| 1 | 1 |
| 2
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 7 |
| 8 | 8 |
| 9 | 9 |
| 10 | A |
| 11 | B |
| 12 | C |
| 13 | D |
| 14 | E |
| 15 | F |
To convert 1368 to hexadecimal, we first divide it by 8, giving us 171 with a remainder of 4. We then divide 171 by 8, giving us 21 with a remainder of 5. We then divide 21 by 8, giving us 2 with
a remainder of 7. Finally, we divide 2 by 8, giving us 0 with a remainder of 2.The hexadecimal equivalent of 1368 is therefore $171_8 = 257_8 = 5A_{16}$.
Option A is incorrect because $7E_{16}$ is not equivalent to $1368_8$.
Option B is incorrect because $5E_{16}$ is not equivalent to $1368_8$.
Option C is correct because $5A_{16}$ is equivalent to $1368_8$.
Option D is incorrect because $5D_{16}$ is not equivalent to $1368_8$.
Option E is incorrect because there is a correct answer.