Originally all opamps were designed to operate on +/-15V or +/-12V - this was universally accepted as a given.
Only more recently have people realised that this is inconvenient since the majority of electronics is digital and 5V was a more convenient supply. Original PCs had a +12V and -12V for several reasons (disk drive motors, serial comms and op-amp/analog interfaces). But now the emphasis is entirely on personal electronic devices where there is no need for such supplies, so a whole raft of low-voltage opamp designs appeared.
Most opamps that can run at 5V don't perform their best at that low a voltage, note, particularly frequency response is compromised. Most rail-to-rail opamps can't actually drive more than a few microamps right to the rail too, so in general you expect even a rail-to-rail opamp to only handle signals from 1.0--4.0V or 0.5--4.5V (on the output side that is). The input behaviour at at least one rail is usually fine (many opamp inputs can handle -0.3V or so on the inputs for instance owing to PNP or JFET input stages.