From https://duet3d.dozuki.com/Wiki/RepRapFirmware_3_overview#Section_Pin_names_for_Duet_2_WiFi_Ethernet :
Duet 2 and DueX heater outputs
bedheat *
e0heat *
e1heat *
exp.heater3, exp.8, !duex.e2heat, !duex.pwm1
exp.heater4, exp.13, !duex.e3heat, !duex.pwm2
exp.heater5, exp.18, !duex.e4heat, !duex.pwm3
exp.heater6, exp.23, !duex.e5heat, !duex.pwm4
exp.heater7, exp.31, !duex.e6heat, !duex.pwm5
So PWM3 is indeed the same control pin as heater5. However, when you say "pwm_3 is connected to E4 which I think associated to heater 4" whereas the heater output labelled E4 is actually heater 5 (heater 0 is the bed, E0 heater is heater 1, etc.)