I am putting in three 6 ft garden doors and two 10 by 5 ft bay windows. I would like too know the minimum size for the headers I need to create above the windows and doors. Please advise.

What kind of load is the headers supporting? You really need to get a code book for your area (or go to the building department) and look it up.

You need to know the type and size of the building and snow and wind loading.

Also based on the area there might be shear load that needs to be replaced with special construction.

I will end up using 2"x10"x12' and build a three section beam for the headers over the windows and 2"x10"x8'..again three pc's over the doors..The room is only 8' x 17' with the doors under the load bearing walls and the bay window in the gable end section. the height of the roof is around 8 feet with a 3/12 to a 4/12 pitch. Snow load where I live are ot really a huge consideration in southern Ontario, Canada and other than a few stronger storm through out the year Wind in not either a huge problem. The window retail outfit told me 2"x8"m