The integrating factor of the differential equation  (cos²x) dy/dx + y = 5 is-

e^tanx

The given differential equation is (cos²x) dy/dx + y = 5

which can be written as- 

  dy/dx + (sec²x) y = 5(sec²x)

Which is differential equation of the form-

dy/dx + py = Q    (Where p= sec²x, and Q= 5sec²x) 

Integrating factor (I.F.) = e^∫pdx

                        ⇒  (I.F.) = exp.(∫scc²xdx)= e^tanx