The length of time that Shepherds Pie will keep in the fridge before going bad is around 4 to 5 days.
After 4 days though the Shepherds Pie will begin to lose it's freshness and begin going bad and after 5 days in the fridge the Shepherds Pie will start growing bacteria and then it will get bad where it will make you sick if you eat it.
If you want to keep the Shepherds Pie longer than 5 days you can and should freeze the Shepherds Pie and when frozen the Shepherds Pie will last for up to a month or two.
The Shepherds Pie even when frozen is best eaten before 3 months although even then it should be still safe to eat as long as there are no mold or other bacteria or bad smell to the Shepherds Pie.
You can reheat the Shepherds Pie in the oven at 350 F to 400 F for around 10 to 20 minutes or until it's heated back up enough for you.