Programming key fob.

if the fob is not for mercury it wont work make sure when buying that it is compatible with your car make and model, look online for instruction how to program your fob keyless remote.

1. Turn ignition from OFF to RUN 5 times within 10 seconds, with the 5th time ending in RUN. Door locks will cycle to confirm programming mode.
2. Within 20 seconds, press any button on first keyless remote. Door locks will cycle to confirm programming.
3. Within 20 seconds press any button on second keyless remote. Door locks will cylcle to confirm programming.
4. Turn ignition to OFF

see if a battery lead is loos

Try this link on programming your key fob. Free Programming instructions for 1999 2000 2001 and 2002

I only have the instructions. If it won't program you may have a problem in the module. In that case see the dealer for testing and diagnosis

. Turn ignition from OFF to RUN 8 times within 10 seconds, with the 8th time ending in RUN.
Door locks will cycle to confirm programming mode. 2. Within 20 seconds press any button on first keyless remote. Door locks will cycle to
confirm programming.
3. Within 20 seconds, press any button on second keyless remote. Door locks will cycle
again to confirm programming.
4. Turn ignition to OFF. Locks will again cycle to indicate end of programming mode.

You are in luck, a 2005 Ford Five Hundred Key Fob Remote is self programmable. Now these procedures can be a bit frustrating at times, so be patient, it's all about timing. If you get it programmed on the first try you are among a very few talented programming individuals! Also, if you need an affordable key fob replacement for your Ford Five Hundred, buy it here:
https://www.keylessentryremotefob.com/Ford-Five-Hundred-Remotes-and-Keys-s/5167.htm

Here are the programming instructions:

FORD REMOTE - THIS PROCEDURE RESETS ALL REMOTES FOR THE VEHICLE. ALL FUNCTIONING REMOTES WILL HAVE TO BE REPROGRAMMED DURING THE PROCEDURE There are a few different procedures that will program your remotes depending on what vehicle that you have. You can find your exact procedure in your owners manual. If you do not have your owners manual you can try any of the procedures below until you find the one that works for your vehicles
Make sure that you don't press the brake pedal at any time during or before the procedure.
Procedure A:
1.Close all doors, then open drivers door and press the Unlock button on driver's door while it is open, insert key into ignition.
2.Turn ignition from OFF to RUN 8 times within 8 seconds, with the 8th time ending in RUN. Door locks will cycle to confirm programming mode. (if the door locks do not cycle, then it was done incorrectly. You must start over by removing key and beginning from step 1)
(Off is the position where you can remove your key, RUN is the position just shy of starting your car.)
3.Within 10 seconds press any button on the first keyless remote to be programmed. Door locks will cycle to confirm programming. If you only have one remote then skip to step 5.
4.Within 10 seconds, press any button on the second keyless remote. Door locks will cycle again to confirm programming. Repeat step 4. for all other remotes.
5.Turn ignition to OFF. Locks will again cycle to indicate end of programming mode.
*If this does not work try the procedure with the door closed.
Procedure B:
1. Fasten seatbelt and close all doors
2. Turn the ignition from OFF to RUN 4 times within 3 seconds.
3. Turn the ignition OFF. The system will chime to confirm programming mode.
4. Within 10 seconds, press and hold any button on first keyless remote. The system will chime once to confirm programming.
5. Within 10 seconds, press and hold any button on second keyless remote. System will chime once to confirm programming.
6. Turn ignition to RUN to exit programming mode.
Please note: All steps should be performed in fairly rapid succession. If you never get the initial chime or door lock cycle, that means the vehicle has never entered programming mode. You should remove key from ignition, open and close the door and start over.

Do you have a keyless entry FOB. If you do replace the battery then program the system. Unlock the doors turn the ignition key to the "ON" position then press either the lock or unlock button of the FOB turn the ignition key off.Now turn the ignition key on again and press either button on the FOB. Turn the ignition off again. Do this 3 times. This initiates programming for the power door locks. Press the lock button of each remote one at a time to be stored in memory. this must be done within 10 seconds of each remote.
3 remotes max. Turn the ignition off and remove the key to complete programming procedure. then test each remote.

Try re-programing the system.
These are the instructions from the service manual.

. Turn ignition from OFF to RUN 5 times within 10 seconds, with the 5th time ending
in RUN. Door locks will cycle to confirm programming mode.
2. Within 20 seconds press any button on first keyless remote. Door locks will cycle
to confirm programming.
3. Within 20 seconds, press any button on second keyless remote. Door locks will
cycle again to confirm programming.
4. Turn ignition to OFF. Locks will again cycle to indicate end of programming mode.

On this model you will have to open glove box and press the tabs on each side so that you can open it all the way open. You will see a 2 wire grey connector behind it.
Turn ignition switch to run postion then take a paper clip or something like that and momentarily short the 2 wires together.
The door locks should then cycle from lock to unlock.Remove the paper clip then press one of the buttons on each remote. When you press the button on the remote door locks should cycle again to confirm that it programed.Then when finished turn off the ignition switch and door locks should unlock to confirm you have exited programming mode.

some possibilities

The power door locks may self-activate or cycle on some vehicles. This may be caused by a misadjusted front door lock linkage, excess solder in the front door power window switch, water infiltration of a potential open wire harness connector inside the front doors, wiring harness chafe on the door check strap, or a damaged Remote Keyless Entry (RKE) key fob.

1) Turn key from OFF to ON eight times within 10 seconds ending in the ON position.

2) After doors lock then unlock, press any button on the
remote being programmed.

3) The doors should lock/unlock to confirm programming.

4) Turn key to OFF and door locks should cycle one last time.