5 13 41 85 257 ___
The answer to this series is 517

lets see how to get there:

the number at odd digit is multiplied by 2 and 3 is added.
the number at even places is multiplied by 3 and 2 is added
so for first term “5” which is at position 1(which is odd).

5 * 2 + 3 = 13

now 13 is at position 2(even)

so 13 * 3 + 2 = 41.

similarly

41*2+3=85

85*3+2=257

So:

257*2+3=517

517 which is your answer