lets say initial speed is s, so time taken will be t = 280/s

its given that is speed becomes s+5 , time will be one hour less, so time would become t-1,

t-1 = 280/s+5

t =280 / (s+5)   + 1

equating first and above equation we get

280/s = 280 /(s+5)  + 1

280/s = (280 + s+ 5 )/(s+5)

280*(s+5) = s* (280+s+5)

280s+ 2400= 280s +s 2 + 5s

s2 +5s -2400 = 0

solving this quadratic equation by quadratic formula we get

s = -51.5  and s = 46.5

since negative value for speed is in valid, therefore speed = 46.5 mph