Focuses on the construction of low-dimensional optimal LCD codes overF5 on the basis of the theory of optimal codes, projective geometry in view of the characteristic of the distance of optimal codes. First, via some known and puncturing, the paper constructs a shortdistance optimal and optimal LCD codes of dimension 3 and 4. Then the theory of projective geometry is used to construct those codes with long-distance. Moreover, with the combination of the known optimal LCD codes and optimal self-orthogonal codes, the paper can construct any long-distance optimal LCD codes. With these methods, all the optimal LCD codes of dimension 3 and 4 can be solved. The theories and methods of constructing LCD codes have a certain of important guiding significance for the study of high-dimensional optimal LCD codes over F5 and those over general field.