Given that sec = 1/cos, we can realize that secx=5 is the same as 1/cosx=5.
From there we multiply both sides with cosx and we get 1=5cosx and now we simply divide both sides by 5 and we get 1/5=cosx, now just get the cos^{-1} of 1/5 which is 78.46 in degrees or 1.3 in radians.