I'm growing potatoes in a 20 gallon container and a 3 foot diameter potato bin in Zone 5 this year and they seem to be growing well. I tried growing 8 in a 20 gallon container last year and they were way too crowded. I've only got 5 in 20 gallons this year, and they still seem crowded. I only got enough for a couple meals last year, but they were great tasting and fun to grow. Even though you are starting late, I think they will still need at least 6 hours of sun a day to grow well. I'd choose short season potatoes if I were you.

I've asked about potatoes in containers on this forum before and never got a response. I'll link below to an old discussion I found that at least gave me some inspiration. I wish you luck.

Here is a link that might be useful: Potatoes in containers

Late in growing also, I was going to put mine in some old tires my son donated to my yard. I had seen where you layer the tires as the potatoe grows and add more soil. At least the tires would be used and no mosquitoes nesting in any standing water. Going to put them in a spot that gets full sun for most of the day.

All my containers are those 35lb scoop cat litter containers. Yes, it's VERY classy! LOL! Probably not really big enough for potatoes but it was just an experiment with some potatoes that were too old to eat. They're blooming now so I guess they are doing something good (I hope!).

I want to try planting in potato sacks but it's probably too late to do them this year. I was late putting anything out this year anyway. I didn't think I could even do any veggies because I'm surrounded by trees. The only place that gets sun is the driveway. Guy at the feed store said "just use containers" and a light bulb went off. (And then I found this forum.)