Sylvia went to dinner with friends. Before a tax of 5%, Sylvia's meal cost $28. Sylvia calculated a 20% tip after the tax had been added to her meal.

What was the total amount Sylvia spent?

The tax on Sylvia's meal was 5%, so the tax amount is 5/100 * 28 = $<<5/100*28=1.4>>1.4

Sylvia had to pay $28 + $1.4 = $<<28+1.4=29.4>>29.4 for her meal after the tax was added.
A 20% tip on the meal is 20/100 * 29.4 = $<<20/100*29.4=5.88>>5.88.
So the total amount Sylvia spent is $29.4 + $5.88 = $<<29.4+5.88=35.28>>35.28. Answer: \boxed{35.28}.