SAE Code P0355
DTC Code 16739
Description Ignition Coil (E) Cylinder 5 Primary/Secondary Circuit Malfunction

SAE Code P0175
DTC Code 16559
Description Fuel Trim, Bank2 System too Rich

SAE Code P0727
DTC Code 17111
Description Engine Speed Input Circuit No Signal

SAE Code P1500
DTC Code 17908
Description Fuel Pump Relay Circuit Electrical Malfunction

Sorry can't help with more. I hope those code descriptions are accurate.

Doesn't sound like a tranny problem but maybe another sensor?