It really depends on how big you want it.
now lets get this straight. 5 gallons isn't Big, but for 5 shrimps? they will get lost and its unlikely you will find them often if you keep any decorations.
10 gallons is a great tank size to start, the Aqueon 10g sells for 10 dollars so often at pet stores.
https://www.amazon.com/Aqueon-Aquarium-Fish-Tank-Size/dp/B01MRCNVSY
petco etc sell them at 1 dollar per gallon ALL the time.
https://www.amazon.com/gp/product/B07GCBRB9Q/
This is the cover I use personally for my 10 gallon.
Now reasons to get a 10 gallon? Personally its easier to decorate bigger tanks, it looks cooler, big driftwoods + some lava rocks, sand, plant substrate in a corner, some pebbles to form a river. You can get real creative with a 10 gallon.
Also Bigger tank = more stability. The bigger the tank, the easier it is to keep it stable. Shrimp THRIVE on stable.
I personally wouldn't recommend bloody mary shrimp, they are VERY COOL, but bloody marys tend to not breed true and need a lot of culling from experience. Also most online sites sell bloody marys, but in actuality? its just cherry shrimp. I've fallen for a few lies and ended up dumping the shrimp into my community tank.
Fire reds are just as cool imo, or blue velvets/ blue dreams look amazing and are a lot easier to keep true to their coloring.
For tank types, shrimps will enjoy every type, but i recommend long tanks instead of tall. Shrimps will climb everywhere for food, but they don't "swim" often. So if you do pick a tall tank, make sure you use up that height by having lots of drift/plants for them to climb on to make use of that space.
With a long tank its much easier to just have some driftwood or plants that rise up slightly.
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You could keep them in a tub not good looking but still if you want a real aquarium you can buy the ten gallon aqueon tanks they're relatively cheap https://www.amazon.com/dp/B01MRCNVSY/ref=cm_sw_r_cp_apa_i_b71JFbX1N2ZG6?_encoding=UTF8&psc=1