Input ripple. Is your input supply actually a stable 5.028 volts? Are you using a multimeter to check or a scope? A multimeter is not good for measuring an unstable supply, it will average out what it sees.
Input capacitor. Is it good? Within the reg's specs? Input and Output capaciters are not always optional. It can depend on your input supply stability or distance. It can depend on your output load. It can depend on your loads operating frequency.
Output capacitor. Consistance loads can deal withou a output cap, but variable loads might require multiple, on top of the regulators required cap if it has one.
Minimum regulating load. Some regulators require higher minimum output loads for prper regultion. Some can be 20mA to 100mA. The bigger the regulator was designed to handle, the higher that minimum tends to be.
Output ripple. Mainly, bad/ovr/undersized caps or insufficient/excessive loads on the output can cause ripple, which will give you the wrong idea of the output voltage with a multimeter. An oscillascope is needed to see what's actually on the line.
Finally, there are tolerances in the typical specs given. Just because it is typically 1.7V drop out, it could actually be 1.55V or 1.85V instead. While a manufacturer tries to meet the typical, different batches might not meet all typical specs and different circuit desgins will change them.
Frankly, giving the reg only 0.028V over the dropout voltage is asking for trouble. Never push a regulator to the line on any spec. A 5.5 or 6V supply, or a 1v dropout ldo would do better.