  We study initial value problem of the $(1+4)$-dimensional
Maxwell-Klein-Gordon system (MKG) in the Lorenz gauge. Since (MKG) in the
Lorenz gauge does not possess an obvious null structure, it is not easy to
handle the nonlinearity. To overcome this obstacle, we impose an additional
angular regularity. In this paper, we prove global well-posedness and
scattering of (MKG) for small data in a scale-invariant space which has extra
weighted regularity in the angular variables. Our main improvement is to attain
the scaling critical regularity exponent and prove global existence of
solutions to (MKG) in the Lorenz gauge.
