What is the rate constant of a first-order reaction that takes 5.50 minutes for the reactant concentration to drop to half of its initial value?

For a first order reaction, the half life is inversely proportional to the rate constant.

The formula is

half life = ln (2) / k = 0.693/k

where k is the rate constant

t = 5.50 minutes

k = ln (2) / 5.50 = 0.126 min^-1

Your rate constant is 0.126 min^-1.