This is my 1st all grain I got a 5gal igloo cooler What the max on grains in this cooler My recipe calls for 14 pounds of grains will this fit in this cooler Simple way it to use a standard of 1.25 quarts of water per 1 lb. of grains. Some recipes call for more or less water but this is a good starting point. so for 14 lbs. of grain you would need 4.375 gal. of water. This is close to max for your cooler but should work and leave enough head space for you to work.
The water should fit, but the water displaced by the grain will add a little less than 1 gallon of needed space, leaving no room to stir, and likely over filling the tun. Go for the 10 gallon cooler. I have been using a 5g igloo for 3.5 gallon batches and it gets very tight when the gravity is a little higher. Great for lagers in the 1.050 range, but had to shift down to 3g for something like Janet's Brown ale at 1.074. YMMV