Attiny45 resets when setting digitalOutput to low
Including the 220Ω resistor with the LED as in the last step? 


...


  My LED can handle 5V, so I used it without, but that cant be the issue


The one thing that "can't be the issue" is indeed the issue! Without a resistor the LED will attempt to conduct a lot of current which will damage both it and the output pin of the processor.

See The care and feeding of LEDs. From that page:


  LEDs are not like normally electronic devices in that you can’t just apply a voltage to them and they work, they have to be fed the correct voltage and current to keep them happy. 


And then:


  There are several web sites and schematics on the web that suggest you can attach an LED directly to an Arduino output pin with no current limiting resistor. They are wrong, and following them will damage your Arduino.




So, by not using a resistor, when the output pin goes LOW it attempts to "sink" current, in order to turn on the LED. Since you have no resistor, it sinks as much as the output drivers can handle, dropping the supply voltage inside the Attiny, which then goes below the brownout level, and resets itself.

Please, when following a circuit, don't just omit bits of it, and then post a question about why it doesn't work. At least follow the circuit exactly, and then when you have learned more about electronics, you can start experimenting.