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Spaceship flies from Earth with large speed. We observe the clock inside the spaceship from Earth with strong telescope.

We see the clock showing 12:00. When we see on the clock 12:05 (in telescope, from Earth), the ship will be further from Earth, so it will take to the light more time to reach us, so on Earth more than 5 minutes will pass. From this I deduce, that for observer on Earth the time on the spaceship goes faster, than on Earth. But if the spaceship approaches the Earth, then we well see 12:05 in less than 5 minutes, and it means the clock on the ship goes slower, than on Earth.

From STO we know, that clock always goes slower in a moving system (for external observer).

Where is the mistake in my thought experiment?

Thanks in advance.