installing ecobee SmartThermostat with Voice Control on older home
Based on that picture, you will not need a PEK, but you'll have to check on the furnace/AC as @ThreePhaseEel has pointed out.
You have:

Power (Red) (R)
Heat Call (Black) (W)
Fan (Green) (G)
Cooling (Blue) (Y)
Common (White) (C)

Matching those up to the ecobee labels should be pretty easy.