My fifth-grade son transferred from Shizuoka to a school in Nagoya.
Literal
Elementary-5th-year [possessive-の] son [subject-が] Shizuoka [from-から] Nagoya [possessive-の] elementary-school [to-に] transferred-in.
転入 (transfer into) is the specific verb for enrolling at a new school — distinct from 転校 (transferring schools in general) and 転出 (transferring out). 小学５年 abbreviates 小学校5年生 (fifth-year elementary student).