Emerging 5G networks will not only offer higher link rates, but also integrate a variety of Radio Access Technologies (RATs) in order to provide ultra-reliable broadband access to a wide range of applications with high throughput and low latency requirements. SDN-enabled dynamic path selection is of critical importance in exploiting the collective transmission resources in such heterogeneous multi-RAT environments and delivering excellent user performance. In the present paper we propose the ‘best-rate’ path selection algorithm for multi-RAT networks with various types of traffic flows. The best-rate algorithm accounts for the radio conditions and performance requirements of individual flows as well as the load conditions at the various access points. We analytically establish that the rates received by the various flows under the best-rate path selection, in conjunction with local fair resource sharing at the individual access points, are close to globally Proportional Fair. Detailed simulation experiments demonstrate that the best-rate algorithm achieves significant gains in terms of user-perceived throughput performance over various baseline policies.