Get Sony A7R II mirrorless at B&H Photo.
Dust on the sensor is generally hard to see at f/5.6 or even f/8, because the rays are not yet highly collimited as they are at f/11 and f/16 (sharp shadow vs diffuse shadow). Of course, big chunk dust (a few hundred microns and larger) can be seen even at f/5.6. And often, detail obscure the spot. It is in areas like sky or other smooth uniform areas that dust becomes obvious.
To test for dust spots, take an image of any uniform surface, like the sky, at f/16. Defocus the lens if the subject has any detail.
As shown below, the Sony A7R II has a dust spot in the sky. I invoked the Sony A7R II anti-dust sensor-shake feature about eight times, holding the camera at various angles in hope that the spot would disappear. It vibrated impressively each time, to no avail, the vibration seemingly too low a frequency to work (ultrasonic would be better).
Taking the lens off, I could see a tiny white spot on the sensor (remember to reverse position from the picture, as with a mirror, up/down are flipped). I never like attempting to clean the sensor with wipes and such (particularly in the field!), and have not done so in years, so I tried something very simple: using a clean new microfiber cloth, I lightly dabbed at the spot just once, and off it came. Which shows that it was not stuck-on in the least, and that the anti-dust sensor cleaning of the A7R II is ineffective at commonplace types of dust spots.
Although this worked, I prefer to never have to make physical contact with the sensor. To that end, I use a large bulb blower—most of the time that works and gets most stuff off. The brand I have used is the Giotto blower—I have a smaller one for field work and a larger one for car or home. Used carefully, a vigorous burst of air can be directed at a very specific spot.