That depends on what you call ground. If the input is referenced to the - supply, but the output is referenced to the center, we would have -5 to 5 output from 0 to 5 input.With you revised R85 connection, a X2 non-inverting amplifier, and a 5V input, what will the output voltage be if not +10V?
Impossible with a positive supply of just +5V.
I think that might be what the TS is doing.
Bob