Will a iphone 5 on Verizon with a bad esn work on at&t?

Will it still work with at&t and T-Mobile
Will GSM still work on Verizon iPhone 5 that has bad esn?

Yes
Yes:}

The phone will work on AT&T or T-Mobile, but 4G data probably won't work.

Nope because they use different cellular radios

Don't you love it when people's answer is that they can't answer but they would like you to answer their question?

No, it will not work. You have a phone with a bad ESN. What is the reason it's a bad ESN? Was it stolen or did somebody simply not pay their bill and get it blacklisted? More often than not, it's stolen. Which means it actually belongs to somebody. You're asking if you can use a stolen phone. Legally, no. Technologically, no again. Sorry, but stolen phones are nothing more than bricks.