Op amps typically run on a wide range of voltages, and the OPA124A is no exception. It will run on +/-5V.
However, it is a poor choice for your application because it is an old design, and not "rail to rail", meaning that the input and output voltages are restricted to be much less than the power supply voltages.
For a beginner photodiode project any modern rail to rail op amp would be a better choice. The MCP6002 (dual, still available in DIP package) should be fine and can operate on a single, 5V supply.