While the AF 70-300 mm f/4-5.6G will not auto focus on a D5200 it will do everything else, like meter and you can set the lens aperture with the D5200 Command wheel and aperture button near the shutter release button.
Many don't read their users manuals very closely (if at all) and don't know all of Nikon's 'baby' DSLRs (D40, D40x, D60, D3x00, D5x00) have a manual focusing aid known as Rangefinder mode. In the D5200 Reference Manual see page 159.