Correct Answer: 5, 4, 3, 1, 2

Solution : Given:
1. Authority   2. Automate   3. Authentic   4. Auspicious   5. Aureole

Step 1: The first and second letters of each word are the same, so move on to the next letter.
Step 2: The third letter of each word is: t, t, t, s, r . Based on the alphabetical order of these letters, we can arrange them: Au r eole, Au s picious, Au t hority, Au t omate, Au t hentic.
Step 3: Compare the fourth letter of (Aut h ority, Aut o mate, Aut h entic). (Authority, Authentic) will come before Automate as h comes before o .
Step 4: Compare the fifth letter of (Auth o rity, Auth e ntic). Authentic will come before Authority as e comes before o .

So, the sequence is Aureole, Auspicious, Authentic, Authority, Automate, or 54312. Hence, the third option is correct.