Is the op-amp supposed to be in negative feedback?
When the transistor is saturated the feedback is negative (an increase in base voltage results in an increase in collector voltage). 

When the transistor is not saturated the feedback is negative (an increase in base voltage results in a decrease in collector voltage). 

Provided V1 > 2.3V the transistor can be saturated. That is true in this case, so feedback is negative. However if the op-amp output drops below the voltage required to saturate the transistor, the feedback becomes positive and it will snap to the +10V rail at the output, with the op-amp output at the negative rail (in fact the transistor Vbe may break  down at that point, restoring negative feedback but it won't be able to get the inverting input down to 5V with typical parts). 







simulate this circuit &ndash; Schematic created using CircuitLab

The above circuit, with the output of the op-amp constrained to >3V or so, will stabilize with 5.00V out. If the op-amp output drops below the voltage required to saturate the transistor then the feedback becomes positive and it will latch with the op-amp output low and the output node at +10V. 



Edit: Mathematically there is a point that is shown in your simulation that won't exist for more than an instant in the real world. It's balanced on a knife edge of positive feedback and will topple one way or the other with 2.188V at the output. If  you do a time domain simulation rather than an operating point, you should see it snap one way or the other.