The job is
Elite TIE Fighter Pilot in The Last Jedi (Star wars)
The number is
And this is
The lego star wars code number for Elite TIE Fighter Pilot. This also fits the title.
The first clue is slightly misleading, as the 5 isn't directly in the middle of the 7 and 2. However as we know a 6 is next to a 2, then 7+5+2+6 = 20. The only number which can be added to this to give a whole number average, and have the second smallest digit as the average is 5. 6 must therefore be last , so the only two options are
No digit is neighboured by two smaller digits, so this rules out 2 because 7 is neighboured by two 5s. This leaves 1. and that gave the answer...
There's a 5 between a 7 and a 2.
Theres actually 2
The second-biggest number is on the far right.
The 6 which is second largest
The average digit value is equal to the second-lowest digit.
7+5+5+2+6 = 25. 25/5 = 5, the second smallest digit
The smallest digit does not divide the largest digit.
2 does not divide 7
You can write it without knowing binary (tricky clue!).
No 0s or 1s
No digit is neighbored by two smaller digits.
No two neighbours are smaller than the one in the middle.
There's a 2 beside a 6.
At the end
Most of the digits are odd.
3/5 are odd