Here are some key topics typically covered at this grade level:

1. Place Value: Understanding the value of digits in a number based on their position (ones, tens, hundreds, etc.).

2. Addition and Subtraction: Solving problems with multi-digit numbers using regrouping (carrying and borrowing).

3. Multiplication: Learning multiplication facts up to at least 10×10 and solving problems with multi-digit numbers using the standard algorithm.

4. Division: Understanding division as the inverse of multiplication and solving division problems with remainders.

5. Fractions: Identifying and comparing fractions, finding equivalent fractions, and solving problems involving fractions (e.g., adding, subtracting, and multiplying fractions).

6. Decimals: Understanding decimal place value and performing operations with decimals, including addition, subtraction, multiplication, and division.

7. Measurement: Converting between different units of measurement (e.g., inches to feet, minutes to hours), calculating perimeter and area of shapes, and solving word problems involving measurement.

8. Geometry: Identifying and classifying two-dimensional shapes (e.g., triangles, quadrilaterals) and understanding concepts like symmetry and angles.

9. Data and Probability: Analyzing and interpreting data displayed in graphs and charts, understanding probability (e.g., likelihood, probability of simple events).

These are just some of the main topics covered in 5th-grade arithmetic. Each concept can be further broken down into subtopics and specific skills. Let me know if you have any specific questions or if there’s anything else I can assist you with!