OOI, I bought a D5200 for my boy to play with so have both the D5200 and D750 to compare.
The D750 is undoubtedly a better camera in every respect; see reviews for the technical data.
That said, the question is would the advantages benefit you ? Only you can tell ?
Also to consider, if you fancy going pro/semi-pro, no matter how good you are I doubt that anyone would be too impressed with someone rocking up with solely a D5200 for a paid shoot ?
Please do not flame, this is not my opinion but just others' perceptions. Getting a pro camera gives you pro kudos.
As well as the D750 which is undoubtedly a fantastic camera you could also consider a used D8xx. D800s, D800es are looking great value used right now.
Just my £0.02.