How to drive high voltage transistor with low voltage op amp?
I've rearranged your circuit to overcome the basic problems in the original: -


Purple box shows an NPN transistor and not a PNP
Blue box gets rid of the diode (the NPN will act like the original diode)
Red box is a reversal of the inputs to the op-amp to maintain correct negative feedback.

Previously your circuit would not have produced more than about 3 or 4 volts at the output due to the op-amp being unable to drive higher than 5 volts. Given that you had three transistors as emitter followers, the output level would be restricted by the upper output voltage that the op-amp could produce.
Now, the added NPN can be turned on or off by the op-amp well within its own power rails.
But, the next problem you will likely face is instability; because I've added gain into the feedback path (NPN as a common emitter), there is every chance that the circuit will become an oscillator at some highish frequency so you might need to add compensation around the op-amp like this: -


In red is an added emitter resistor - choose a value that is no less than one tenth of the resistor connected to the NPN collector
In red is a frequency compensation circuit that can reduce the open-loop gain and produce a a roll-off of no more than 6 dB per octave up to the unity gain point. This should ensure that the phase angle doesn't reach the oscillation point.

Simulation circuit
I used Micro-cap 12 to to a basic simulation of the DC levels to see that it functions: -

It produces 10.011 volts on the output for a reference input (V4) of 2.5 volts. Ideally it would be 10.000 volts but the op-amp I chose is a bit basic (LM324) and it has a significant input offset voltage that adds an error. The load is 100 ohms (R6) and it is drawing 100 mA as expected.
I used a TIP120 Darlington for the main power transistor.
Now If I look at the transient plot I get this: -

In other words it's significantly unstable but, I chose R2 (emitter resistor) to be 100 ohms to purposefully entice it to be unstable - If I make R2 into 1 kohm I get this: -

It looks fairly stable but, if I add 1 uF output capacitance across the load this happens: -

Not so stable now is it. So, integrating feedback around the op-amp will probably help. 220 pF and 1 kohm added to turn bare op-amp into an integrator: -

It's just at the cusp of being stable so I'd go for something in excess of 1 nF to kill the problem off.