Crown vic transmission problems
 

I have a 2005 Crown vic sport with 118k miles on it. Over the winter I noticed that it was taking a few seconds for the transmission to engage when shifting from reverse to drive. The trans also has a very slight whine that I can only hear when the radio is off. The fluid and filter has been changed about every 20K since new. Any thoughts?

Has the fluid level been checked to make sure it is correct?

Fluid Level
 

Yes it is full and doesn't leak a drop. It has also been changed since the symptom showed up. I have been using Castrol Mercron V. It is worse when it is cold.

There are certain sealing rings that when pressure is applied a clutch piston moves to compress a series of apply discs and now the power gets transferred out to the output.
When these sealing rings get stiff or leak until they get warm a problem like what your vehicle is showing surfaces. This is only one reason, in my opinion, and may not necessarily be the problem here.