It would be difficult to analyze such a problem without a first hand driving test.
Simply as an example, I could ask , when gear shifts from 5 to 4, it is natural for rev to jump. But I sense, you know that, and hence used the word "abnormal".
Basic understanding is, slip from 5 to 4 can easily be if the engine needs more power than it does on 5. And that can happen for many reasons, from air intake to injector or valve or calibration or even tuning not well set, and the torque due is lost but more prominently noticed when the car is on the 5th gear.
And it is not simple as that. There could also be a malfunction somewhere along the lines of OD (over-drive), air flow sensors, knock sensors to the ECU (the chipboard that controls the electronic coordination).
But I would firstly suggest test drive by a professional, and RUNX should be easily electronically scanned for very accurate depiction.