mathmo

Ah, I may have misread. I thought it was 3 seconds to turn the slice over in total. But it seems you mean that it takes 5 seconds to remove, 3 seconds to turn and then another 5 seconds to put it back in. That changes things ...

We have to replace everywhere I have put a 3 with 5+5+3 so this adds 20 seconds to our time, making it now 2 minutes 16 seconds. I wonder if there is a quicker way then with switching slots instead of turning, I'll have a think ... or perhaps someone might beat me to it?

Ok, I've had a think and it gets tricky depending how you interpret things.
The following is faster than the above and nasty ...

You may want a diagram, I suggest two vertical lines representing the two slots, marked off in 5 second intervals.

Let's call the slots 1 and 2 and the slices A, B and C. Put slice A in slot 1 for 30 seconds. and at the same time slice B is in slot 2, but for 15 seconds. After those 15 seconds, slice B is removed and slice C is put in slot 2 (10 seconds) 5 seconds later, we remove slice A then put slice B in slot 1 for 30 seconds. Now slice C only needs another 15 seconds and is then removed and replaced by slice A which is toasted for 30 seconds. 5 seconds after slice A is put in slot 2, slice B is removed from slot 1 and replaced by slice C. 15 seconds later slice A is removed from slot 2 and replaced by slice B for the 15 seconds that was missed at the beginning. 5 seconds later slice C is fully toasted, and another 10 seconds and slice B is toasted.

Now, we have used 2 minutes, which is the minimum since every slice needs 30 seconds to toast one side and 10 seconds to be replaced. Since there are 6 sides, this is 6*(30+10) = 240, but there are two slots, so this is 240/2 = 120 = 2 minutes.

Fingers crossed this is right...