In large bowl, dissolve yeast and 1 tablespoon sugar in 1¾ cups lukewarm water.
Whisk oil into yeast, then beat in 4 eggs, one at a time, with remaining sugar and salt. Gradually add flour. When dough holds together, it is ready for kneading.
Turn dough onto floured surface and knead until smooth. Clean out bowl and grease it, then return dough to bowl. Cover with plastic wrap, and let it rise in a warm place for 1 hour, until almost doubled in size. Dough may also rise in an oven that has been warmed to 150-degrees and then turned off. Punch down dough, re-cover and let rise again in a warm place for another 30 minutes.
Divide up your dough to either bake or freeze. If baking, braid, and beat remaining egg and brush it over your challah. Let rise for another hour.
Preheat oven to 375-degrees, bake for 18-22 minutes.
Recipe by the minimalist table at https://www.daraboxer.com/theminimalisttable/shabbat-challah/