The product of first three terms is 13√13. Fifth term equals 169/64. Find the first term. 5 terms

A little like 2011 ARML I-3 Finite Geometric Progression
Linguistically, the common ratio of a geometric sequence is quotient of a successor and its predecessor. Math-Only-Math(explain it to me like you would explain it to a kid) covered this topic clearly.
Congrats to Singaporean Xu Linfeng for first place finish! Rhinoceros Mathematics