Weird message on Iphone 5s, grey screen w white dismiss button

same problem, no solution???

That happens sometimes if you try to hit a combination of numbers such as that to get your IMEI but instead trying to access a function that is not supported by your carrier

For example dialing *#06# will get you your IMEI number - doing this will actually reproduce the grey screen you speak of - but also show you a number

The question I would have is - was your phone ported from one carrier to another? If so it may be programmed to do some self diagnostic that is no longer available hence the message

Yes, the phone was ported from one carrier to another.

Yes, dialing *#06# reproduced de grey screen, a number and a dismiss button.

Can you help me to solve the problem?

The only thing i can think of is:

Back up photos / documents and contacts

Then restore iPhone as new

Reload your stuff

Do not restore from backup as that will bring the previous programming that is causing this

Up to you if you want to go through with it

I say wrong, my 5s is originally from Apple, not from a carrier

Was the phone restored to factory settings before being given to you? That would be a good idea.