Let's ask the boy who lives next door.

Literal

Next [at-に] live-ている boy [to-に] ask-[try-てみよう].

聞いてみる ('to try asking') uses ~てみる ('try doing X'). The volitional みよう ('let me try, let's try') makes it a self-directed or inclusive suggestion. 隣に住んでいる is a relative clause modifying 少年 ('boy').