Question 237566
This series is really 2 different series mixed together

3,5,5,19,7,41,9,....

Start at the first number and then take every other one
3,5,7,9 ... it's easy to see the next one there is 11

Start at the second number and take every other one
5, 19, 41 
I don't see a strict easy pattern jumping out at me here. 
So let's think about using something from the first series.
3^2 = 9   9-5 = 4   
5^2 = 25  25-19 = 6
7^2 = 49  49-41 = 8
hmmm maybe we are into something
9^2 = 81 81-x = 10
x = 71
I am going with 71