LM358 output will not rise above about 3.5 V on a 5 V supply: is the op-amp faulty?

The part is behaving as specified. The LM358 output stage pulls up through NPN transistors arranged as emitter followers, and they need about 1.5 V of headroom, so the output cannot rise above roughly V+ minus 1.5 V. On a 5 V supply that is about 3.5 V, which is exactly what you see. The row to read in the datasheet is output voltage swing, with its load condition.

The low side is better: the output can get within a few millivolts of ground, but only when the load is a resistor to ground and the current it has to sink is tiny. With a load connected to the positive rail it stops several hundred millivolts above ground.

There is a second limit on the same part that catches people with buffers. The input common-mode range extends from ground up to V+ minus 1.5 V at room temperature (V+ minus 2 V over the full temperature range). On 5 V the inputs are only valid up to about 3.5 V.

In your gain-of-2 circuit both inputs sit at the sensor voltage, 2.5 V at most, so the inputs are fine and only the output clips. In a unity-gain follower, or any circuit where the inputs must go near the positive rail, the input stage gives up first and the output can behave unpredictably.

Three ways to get the range you want:

• Use a rail-to-rail input and output CMOS op-amp, such as an MCP6002-type part, that is specified for 5 V single supply. It is pin compatible with the LM358 in the 8-pin dual package.
• Run the LM358 from a higher supply, 9 V or 12 V, so that 5 V is well inside its swing, and protect the ADC pin with a series resistor and clamp so it can never see more than its supply.
• Keep the LM358 on 5 V and lower the gain to 1.3, so 2.5 V becomes 3.25 V. With a 10-bit ADC referenced to 5 V you then use about 665 of the 1023 codes.

Even with a rail-to-rail part, do not plan on exactly 0 V and exactly 5 V. Rail-to-rail output means within a few tens of millivolts of each rail at light load, and the gap grows with load current; the datasheet gives the swing at a stated load resistance. If the ADC reading must reach true zero and true full scale, design the signal to span something like 0.1 V to 4.9 V and correct the offset and gain in software, or use an ADC reference slightly below the supply.

Also keep the ADC input happy: a small RC filter, for example 1 kΩ and 100 nF, between op-amp and ADC pin isolates the op-amp from the sampling capacitor's charge kicks.