P28 PLT HAS A TXWY EXCURSION AND STRIKES TXWY LIGHTS AT HLG.

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THE APCH; LNDG; AND ROLLOUT WERE GOOD. WHEN CLRED TO DEPART THE RWY I FELT THE ACFT WAS TRAVELING SLOWLY ENOUGH TO EXIT ON TO THE TXWY. I WAS STILL APPLYING SOME BRAKING ACTION; THE ACFT WAS TRAVELING APPROX 15-20 MPH WHICH APPARENTLY WAS STILL TOO FAST TO MAINTAIN THE CORRECT TRACK ON THE TXWY CTRLINE. ALTHOUGH; INITIALLY I FELT I HAD THE ACFT UNDER CTL; WHEN I RECOGNIZED THE ACFT WAS STILL TRAVELING TOO FAST; IT WAS TOO LATE TO AVOID RUNNING OFF THE TXWY AND INTO THE GRASS. THE APCH; LNDG; WIND; WX; LENGTH OF THE RWY; AND TFC WERE NOT A FACTOR. THE ACFT PROP WAS DAMAGED WITH A NICK APPROX 5/32 OF AN INCH ON ONE BLADE AND 4 OF THE BREAKAWAY TXWY LIGHTS WERE KNOCKED DOWN. AFTER AN INSPECTION OF THE ACFT WE TAXIED TO A PARKING SPOT AND TIED THE ACFT DOWN. WE FELT THE NICK MAY PRESENT A SAFETY HAZARD AND SHOULD BE INSPECTED BY A MECH. SUPPLEMENTAL INFO FROM ACN 703104: ALTHOUGH SPD AT START OF TURN SEEMED FASTER THAN NORMAL; STUDENT WAS EXPERIENCED AND FAMILIAR WITH OP OF CHEROKEE 140. IN HINDSIGHT; I ALLOWED MYSELF TO BECOME TOO COMPLACENT WITH THIS PHASE OF OP; AND DID NOT FULLY RECOGNIZE THE DEVELOPING SITUATION UNTIL TOO LATE TO AVOID RUNNING OFF OF TXWY PAVEMENT.