Lithium, beryllium, and boron are elements with atomic number 3, 4, and 5, respectively. Even though they are three of the five simplest elements, why are they rare compared to many heavier elements?

These elements are rare because:

Helium fuses into the carbon by the combination of three helium nuclei (Z = 2) and one carbon nucleus (Z = 6), therefore bypassing elements with Z = 3, 4 and 5 which are lithium, beryllium, and boron respectively. Therefore, the fusion processes in cores of the stars do not form these three elements.