The boiling point of elements increases down the group mainly because the mass increases.
Melting point, on the other hand depends on the energy required to overcome the inter-atom interactions and break the molecules apart. At the top of the group, we have nitrogen which deadly forms covalent bonds and the molecule is N2. Then we have phosphorus which has a tendency for covalent bonds but now the molecule is P4 causing the requirement of a larger amount of energy to break it. Arsenic has a bigger array of atoms like in silicon hence making it tough to break them apart. Now as we go further down the group, the metallic nature of elements increases due to poor shielding by newly introduced d and f orbitals. The loosely held electrons give rise to weak interactions. Arsenic is a metalloid, so it is the point of inversion of the strength of interactions. Hence, the melting point increases up to arsenic and decreases down till bismuth.