The game checks whether it is legal to cast a spell before costs are determined or mana abilities are activated while casting it. If cards are removed from your graveyard after that point, such as by exiling Jack-o'-Lantern from your graveyard to pay for its mana ability, this won't affect whether you can legally cast Graveyard Shift, even if that reduces the number of mana values in your graveyard to below five.

If an effect allows you to cast Graveyard Shift from your graveyard, you may cast it any time you could cast an instant if you have five or more mana values among cards in your graveyard immediately before you begin to cast it, even if moving it to the stack would reduce that number to four.

“Five or more mana values among cards in your graveyard” means there are at least five mana values among those cards.

The mana value of a split card in the graveyard is the total mana value of both halves of that card. It does not have two mana values.

The mana value of a double-faced card in your graveyard is always the mana value of the front face.

X is 0 when determining the mana value of a card in your graveyard.

The mana value of a land card is 0.