Trouble with a Toyota Corolla?

If it is a lot of smoke I would have a difficult time believing that the lower half is gone. It's burning something if it's a lot of smoke. the reason why it is going away after 5 minutes is the motor is warming up and the parts inside are expanding. I would take it to a shop (Not the guy you took it to) and leave it over night. Have them do a compression test in the morning with out starting it up and see what the readings are. then let them drive it to warm it up and have them run the compression test again and see what the readings are. the tests should give them an Idea where the problem is coming from. they could also do a wet Dry compression test with out ever having driven the car. but it would be good to have them see the smoke. Since you said this only happens when the motor is cold I would suggest leaving the car over night.

attempt turning the most important to the on position (sprint lights no crank) for 10 seconds. turn key off and repeat to on position for 10 seconds 4 situations and then attempt starting up the motorized vehicle. If it begins usually because it would want to you've a challenge with the gasoline pump which has a valve in it that retains gasoline pressure from bleeding off.

it could be a blown head gasket take it to a diffrent mechanic and get a second opinion it could be the rings or cylinders if it didant go away ??? good luck mabey take it to toyota

if he did a real valve job ask him what kind of valve seals he put in... he better have an answer... it may have nothing to do with valve job... could be bad rings.. get a compression check to find out.

Sounds like the head gasket is bad.

Also sounds like the mechanic is ripping you off.

Take it to a dealer.