My personal grow is in 100 gallon beds, and the grows I've been paid to construct and consult on all grow in 60 to 150 gallon troughs...so my pot recommendations tend to be far from conservative lol.
I do not grow autos so unfortunately I'm not 100% sure on how to relate my experience to yours.
I can only say if it is your intention to shoot for a water only style grow, than five gallon pots will be to small. I would also recommend a 15 or 10 gallon pot.
But I don't know about autos since you've got a limited growth period. it might be better to have a smaller pot where the roots fill out quicker and then you just feed a liquid solution? I've been raising mothers and doing clones my whole grow career, I apologize my knowledge of autos is pretty stunted. I can only tell you why I do what I do, I hope it helps.
basically, say my basement height caps out at 10 feet, so im never gonna grow my plants higher than 6 feet.
I can grow the same two six foot plants in a 7 gallon pot, or a 15 gallon pot. Their root balls are where the difference is. The smaller pot will want to have the same size root ball as the bigger pot, since it has less pot to move around in, it will fill in every crevice of space in the soil and eat up all the available nutrients. You can top dress or liquid feed after this, it's a simple solution. But the plant in the bigger pot, the roots will have more soil to get into, so your nutrients in the soil tend to last longer. highly soluble anions like nitrogen still tend to need some reapplication, but a good base of compost, along with some neem cake seems to take the N a lot further.
But again, for autos you might be better off not following my approach. something with more water soluble nutes might be better suited to the limited growth time line.