This isn't quite an ELI5, but ARRL has a 2004 article on FM fundamentals; it's five pages intended for a beginner ham radio operator, but applicable to all FM applications nevertheless. It also discusses four different ways to receive FM.

But to answer your question directly:

The frequency of the FM signal at any instant in time is called the instantaneous frequency. The variations back and forth around the carrier frequency are known as deviation

FM can also be detected by a PLL. As shown in Figure 6, the PLL’s natural function of tracking a changing input frequency can be employed to generate a voltage that varies as the input frequency change

In a nutshell, FM only ever has one instantaneous frequency at a time, which dances around the nominal center frequency (aka carrier). So the receiver has to detect the instantaneous frequency, relative to the carrier.

To actually recover the original signal, the receiver must also account for the modulation index used by the transmitter, which describes how much the output will deviate for a given input frequency. The modulation index is usually standardized for the application, such as FM broadcasting, amateur radio FM, walkie talkie FM, etc.

Because a larger modulation index means the same input signal will result in wider deviations, more RF bandwidth is used, spreading the signal wider and generally improving noise immunity.