The answer you really wanted to hear?
13:00 on Treadmill 1% grade --> Track/ road 5k is not doable. There is a major difference in how these tests are conducted. 1) On treadmill, it is just you and you alone. No one to visually see that you are going 13:00 for 5k.
2) You're claiming theoretically you can beat most of America in the 5k. Currently the fastest 5k in the world is 13:21 by Sean McGorty of BTC. Proof enough that you running 13 flat on treadmill is not doable versus professionals who are doing it on an indoor track. Sure there are turns on an indoor track and outdoor veruses none on treadmill but realistically how much different in time would that be?
3) The fastest 5k times last year only 8 broke 13 and 9th was 13:01 outdoors with perfect weather conditions i.e. roughly 45-55F with good competition. (IAAF has this data so its all fact)
4) If you're running 3:57 for a mile why aren't you running professionally/in big races i.e. millrose, BU, outdoor big races. I'm sure a lot of us would like to see that (not doubting your ability) happen as the phrase goes, actions speak louder than words.
5) Also effort alone condition or not...Treadmill keeps pace but the fastest a treadmill gets Is 4:40/mile pace which is 14:30 5k pace...Plus its assuming you maintain effort throughout each mile excluding startup of initial settings....
So to answer your question, How realistic is a 13:00 5k on treadmill? Its not realistic at all...The biggest reason why is because do you ever see WR attempts being done on treadmills? Do you ever see elite 5k times on treadmills? All these make for solid reasons on why 13 flat on treadmill for 5k is simply just not doable. Possibly in future but to todays standards, Never. Best of luck in your endeavors though and I hope you do run low 13s for 5k. America could always use someone with great optimism in the running community. Have fun and good luck.