Not eli5, but a comparison to the Riemann Hypothesis (RH).

RH says the Riemann-zeta function has no zeros along the line (1/2) + iy in the complex plane.

The Lindelof hypothesis says that the number of zeros between (1/2) + iy and (1/2) + i(y+1) is much smaller (little-o) than log(y) as y grows.

So it can be thought of as a weaker version of RH, but still very very difficult. The fact that Lindelof has been an open problem for over a hundred years (and is an non-trivial weakening of RH) speaks to how difficult RH is as well.

Like RH, Lindelof implies things about primes, and also (like RH) has lots of implications about lots of interesting prime-like (irreducible) objects in different spaces.