I have calculated the transfer function of such systems many times, but now i feel like I`m going around in circles. I have drawn a few help-signals to help me solve it, but they are dependent of one another and no matter how many times I replace the values, I just finish where I started. I must calculate the total transfer function of the system from the attached image. The coloured lines are the help-signals that I added and their description is below. Any help is appreciated]1
Not a full answer; just some assistance....
Just one simple block diagram re-arrangement gets you an improvement (as per LvW's comment to your answer): -
Notice the added red block contans \$1-H_1(s)\$ and this removes the summing node just in front of \$H_3(s)\$. I'm assuming that was an intentional negative sign on the summing block I removed hence the negative sign in the new block I added.
Sometimes you have to add stuff to simplify but other folk may choose a different starting point.
The next thing to do (in my opinion) would be to re-arrange things like this: -
Hopefully I've not screwed up anywhere but I'm sure if i have there'll be someone eager to point it out.
Can you take it from here?