According to NASA once again, a potential trip to Mars would have a cruising speed of around 39,600 km/h (24,600 mph) with current technology. If we, naively, assume that the rocket goes straight to Neptune (i.e. the travel distance is *only* 4.5 billion kilometers) it would take approximately 4,735 days or 13 years.

The problem with this calculation is that both, the trajectory would not be straight, as the rocket path would most likely follow the gravitational pull of multiple celestial objects along the way, and, most likely, the trip would be timed so that the rocket travel the shortest distance possible, which most likely decrease the overall fly time between Earth and Neptune.
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