The resulting voltage drop is a gain error of 0.1/5 k (~0.0019%), well over 1 LSB (0.0015% for 16 bits). And this ignores the issue of the return path! It also ignores inductance, which could make the situation worse at high frequencies.
So, when dealing with precision circuits, the point is made that even simple design items such as PCB trace resistance cannot be dealt with casually. There are various solutions that can address this issue, such as wider traces (which may take up excessive space), and may not be a viable solution with the smallest packages and with packages with multiple rows of pins, such as a ball grid array (BGA), the use of heavier copper (which may be too expensive) or simply choosing a high input impedance converter.
But, the most important thing is to think it all through, avoiding any tendency to overlook items appearing innocuous on the surface.
