Final answer:
During a routine 5,000-mile-interval inspection, the air filter should be checked. It is essential for ensuring the vehicle's engine receives clean air, which is vital for optimal performance and efficiency.
Step-by-step explanation:
A routine 5,000-mile-interval inspection for a vehicle typically includes a variety of maintenance checks to ensure the vehicle is running efficiently and safely. The correct answer to what should be checked at this interval is: A) air filter. The air filter is a crucial component of the vehicle's engine as it filters out dust, dirt, and other contaminants from the air before it enters the engine. A clean air filter is important for maintaining proper air flow and engine performance. While checking the cabin filter, power steering fluid filter, and transmission filter can also be important, they are not typically included in a 5,000-mile-interval inspection.