iPhone 5 with passcode, but my ex was able to read my texts....

Nope! Totally disabled.

I have several times. He's never known any of my passcodes, yet it continues to happen.

No. I have done all the checks and research for that. I was even shown a screenshot of some of my texts - a screenshot from "my" phone. The time said 5:46 AM, and he told me he has someone he can call and get whatever he wants. I have doubted this in the past, but he continues to hack into messages and save them. I've seen proof of this, and he knows things that I've never told him. My phone is never out of my sight. He said he has "people" who can do that sort of thing remotely. He is saving "incriminating" texts in an effort to make me lose my job if our breakup gets messy.

Do I have a legal foot to stand on here?

It was definitely a screenshot of my phone. There's no other way he would have even had that phone number - the text wasn't with someone I had in my contacts.

The police can't do anything, since he won't admit it and seems to have covered his tracks pretty well.

Does anyone have any ideas?

Last night he said he had someone he could call, he could read my serial number to them, and they would tell him my latest passcode. He said changing my phone number wouldn't help.

Then tonight, he said that my texts are being delivered elsewhere as well as to my phone.

Whichever it is, he is obtaining access to my phone and I don't know what else to do.

Please keep the good ideas coming!

He would know the apple ID, but not the password.