A modem is a modulator and demodulator. It's what takes digital bits and turns them into analog signals to send them across the wire.
Frequencies are a limited, valuable resource. Different stakeholders have officially claimed frequency boundaries.
The Shannon limit is a mathematical equation demonstrating the theoretical limit of data rate on a random channel; in particular, a corollary is that increasing the signal power has diminishing returns on the data rate.
We are actually right near this limit right now, so there's not a whole lot we can do to drammatically increase data rates.
And no, 5G is not magic. There's not really much innovation there.
At the link level, discrete IP packets need to be framed (that is, where does the packet start and end?)
Byte stuffing: flags at the start and end, but does require escaping flags in payload
Bit stuffing: causes byte mis-alignment so this isn't used in many protocols.