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.