The general objective of teaching different types of lines in grade 5 math is to help students understand and identify various types of lines, such as horizontal, vertical, parallel, perpendicular, and diagonal lines. This knowledge is important for developing spatial awareness, geometry skills, and problem-solving abilities. By learning about different types of lines, students can also enhance their ability to analyze and interpret geometric shapes and patterns. Additionally, understanding lines is a fundamental concept that lays the foundation for more advanced mathematical concepts in higher grades.