SD Card wont work, no matter what i try

You are right, it should work fine, since i never heard, that it did not work for anyone.
I checked the wiring about 10 times, i rewired it several times, it never worked, so im about 100% sure, there is nothing wrong with the wiring. As exchanged the wires as well, still no work. The Breadboard also works fine since i tried with and without breadboard at different spots, as well as i checked if the VCC and GND of the module works with a LED.

I also thought, that the UNO is the problem, but if i use the pins to send and recieve data for other applications it works fine as well.

I get this error:

if (!card.init(SPI_HALF_SPEED, chipSelect)) {
    Serial.println("initialization failed. Things to check:");
    Serial.println("* is a card inserted?");
    Serial.println("* is your wiring correct?");
    Serial.println("* did you change the chipSelect pin to match your shield or module?");
    return;

I also tried a other Code, with SD.begin which also did not work for me.

Power is provided from the Arduino 5V directly to the module. Formatted with SDFormatter in FAT.

I apparently am not able to upload a picture, but as said i just connected the module. VCC and GND directly to Arduino 5V and GND, rest as in the code i posted, with CS to pin10. I decided to get another module, since they are not that expensive, just to make sure that it isnt the module, that is not working. Or is there any other way to find out whether the module itself works or not?