So that's just a tad under 13 pounds. I'd go with 1.25 quarts of water per pound of grain, so you can mash out.
For the mash, 13 x 1.25 quarts/pounds would mean using 16.25 quarts of water for the mash. You could call it 4.5 gallons to make it easier!
Mash in with 4.50 gallons of water and hold at 152 for 60 minutes. (Use water approximately 15 degrees warmer for your strike water- so 4.5 gallons of water at 169 for the mash in a preheated mashtun). Each system is different, so have a little boiling water handy and a few ice cubes, in case you miss high or low!
After an hour, stir in 7 quarts of boiling water and stir well to mash out.
Then you can vorlauf and start your sparge. Since your grain should absorb about 1.5 gallons of liquid in the mash, you can plan about 1.25 gallons of sparge water needed but have more ready so you can make sure you hit your boil volume.
I'd be surprised if starting with 6 gallons in the boil kettle would work for you for 5 gallons in the fermenter. You'll be boiling for an hour, plus have some shrinkage in cooling. I'd start with at least 6.25 gallons, preferably a bit more so that you end up with enough beer in the fermenter in the end.