The application of locally repairable codes (LRCs) in distributed storage system can improve the efficiency of repairing lost nodes. The optimal quinary LRCs with a code length of not more than 31 are studied and Four kinds of optimal quinary LRCs and their characterization are given. Firstly, parity check matrixes with good performance of LRCs are constructed by using the distance optimal linear codes and special codes such as Simplex code. For the known LRCs, other LRCs are given by means of shortening, puncturing, adding or deleting column vectors. The results show that these optimal LRCs have minimum distance 2≤d≤8 or d=10 and all the results respect the Singletonlike bound. These results have reference value for the construction of other optimal quinary LRCs and optimal LRCs over general fields.