Problems calculating torque for a motor opening a door
Your calculations assume the whole weight is applied at the end of the lever. In fact, it will be roughly halfway there, at 0.25m

Also, since it will be horizontal at the highest point you don't need any trigonometry here. Your minimal torque is simply the weight of a door applied at half the door height, or 5 kg at 0.25m. Which is 1.25 kg-m or 125 kg-cm.

Of course you need more than that for reliability, say 150-200 kg-cm. While it is possible to find geared motors like that, they will be either a) slow, b) high current, c) expensive or d) all of the above.

Now it is good time to recall that garage openers have tiny motors compared to the weight of the doors. That is because majority of the lifting is done by a counterweight or a spring.

So, my suggestion would be to use good spring-loaded door and relatively small motor with worm-gear, picking up the small portion of the weight. Automotive 12V power-window motor mentioned here seems to be good fit for applications like this. You can also find one of the possible simple schematics for controlling the motor at that link, no MCU necessary.

Note that when designing spring assistance you do need take into account the angular position of the door. This is simple mechanical problem and you should be able to find examples or calculate it yourself. The basic idea is that the point of application of relatively constant spring/weight force should move further from the pivot, exactly following the door's center of gravity moving further from vertical as door is rising.

Also note that regardless of the small torque of the motor required, the gearbox and all connectors should be strong enough to keep the door in fixed position should something happen with counterweight system.

Finally, make sure you have fuses in your electrical wiring (separate for each direction!) rated close enough to normal working current so that if a limb accidentally gets in the way the motor will stop rather than causing injury. 



Note that 3PDT switch should be rated for both mains voltage and motor current. End switches should be rated for mains voltage and current and should be snap-action type to prevent extensive arcing.