I have a two year old 5hp Honda enigne on a Troybilt frame. When the choke is engaged, the engine starts on the first pull. After the choke automatically shuts off, the engine dies immediately. Repeating same thing happens. Will not contiue to run.

Clean the carburetter out... its got a clogged fuel jet, likely from varnish buildup from being parked with fuel over the winter.

Or less likely a vacuum leak.

Thanks, I have been reading on line that it could be the plug and thought that was strange since the mower would run while choked.. Now the big question is how to get the carburetor off the mower...

I'm not familiar with that specific model. But small engine carbs are typically help on with two screws plus whatever the airfilter is attached with. If you have access to get the float bowl off with some spray carb and choke or throttle body cleaner you can get the crud off without removing it. But you WILL need a proper solvent.