How do we calculate bandwidth from signal formula? How can we calculate the bandwidth of distinct signals like this?
I guess the right answer is 90 - 10 = 80 Hz. But I have a hard time understanding why is this calculated in that way. I thought the bandwidth is calculated by the diversity of signals and since there aren't in-between frequencies like 11, 12... in the image there are 5 signals, shouldn't the bandwidth be 5 Hz? What am I missing here?
Your intuition is basically correct.  I'm sure they want the answer of 80Hz because that is the bandwidth that you would need to carry these 5 waves, but pure sinusoids that aren't modulated at all can not carry any information.  If they don't carry any information then they are infinitely narrow.  (0Hz rather than 5Hz).  You could modulate them individually to higher frequencies and put them very close together with any loss of information.