In a medium bowl, add the honey and brown sugar to the warm water and whisk. Sprinkle the yeast on top, cover and set aside for 8-10 minutes to allow the yeast to bloom.
In a large bowl or stand mixer with dough hook, add 4 ½ cups flour and mix with salt before adding the bloomed yeast mixture.
Mix on low speed or by hand until combined.
Add the remaining 1 cup of flour. The dough should pull away from the sides of the bowl.
Knead for 3 more minutes until the dough is elastic and smooth.
Turn the bowl upside down covering the dough on the counter or put the dough in a bowl and cover with a kitchen towel or lid. Allow the dough to rise until doubled in size, about 60 minutes.
Line a baking sheet with parchment paper and set aside.
On a floured surface, turn dough out and cut in half.
Stretch and pat or gently roll each half into a rectangle.
Roll up lengthwise and press down gently to push out any air pockets. Pinch the ends and tuck under.
Transfer the two baguettes to the baking sheet, spacing them apart, and slash diagonally with a sharp knife. Allow to rise another 30 minutes.
Preheat the oven to 400°F.
Brush with egg wash and bake for 18-20 minutes.
