Confirming the quality of your fuel should be easy, and this should be done first.
The big thing to check here would be the guide vane min/max angle, and bleed valve min/max angle.(KF_BV_Srg_FGEN_NGP and associated KF's)(KF_GV_Srg_Sched_FGEN, and associated KF's) These should be set by the OEM during commisioning and not changed by anyone else. If this is new equipment, both of these should be powered by PECC electronic actuators. The min/max angle for both of these should be on the test report and engine data plate. Confirm these values with what is in the PLC logic. These are both electronically limited and this is where they are set.
I would also use the "Histrical data Analyser" on the HMI to view the actual angle they both had at the time. With the machine in T5 control, both of these values should be maxed out. (Fully closed bleed valve, Guide vane angle on limit).
You mention bad T5 spread. What is the spread like when the machine is cold? If the spread is still bad then it could be faulty probes, wiring, or Isothermal plate.
Hope this helps.