The sum of two log functions with the same basis can be expressed as follows:
[tex]\log _ax+\log _ay=\log _a(x\cdot y)[/tex]In this case, we have a = 5, x = 3, and y = 8. Therefore:
[tex]\log _53+\log _58=\log _5(3\cdot8)=\log _524[/tex]So, option C is correct.