Trying to take octaves for granted is like trying to take fast playing for granted: you are trying to take something for granted that should not be taken for granted.
Let gravity help you sink into the keys, and let the natural recoil of the piano keys "bounce" your hand back off the keys, much like dribbling a basketball on the ground.
As for playing octaves with other fingers: do NOT try to "stretch" per se; tilt your wrist and tuck your elbow into your body to help place your finger on the correct spot.
Not every one of us have a gigantic hand like Garrick Ohlsson or Sviatoslav Richter. So, how do we play something like Chopin's Etude Op. 10 No. 1, No. 9, No. 11, Op. 25 No. 1, Op 25 No. 3, No. 4, etc.? Answer: by using the help from the elbow and the wrist.
Doing 1-5 is definitely easier to do on the white keys.
Doing 1-4 and 1-3 is definitely easier to do on the black keys.