from fastapi import APIRouter, HTTPException

people = [
    {"name": "Alice", "age": 55},
    {"name": "Bob", "age": 45},
    {"name": "Charlie", "age": 60},
    {"name": "David", "age": 35},
    {"name": "Eve", "age": 52}
]

router = APIRouter()

@router.get("/people")
async def get_people_over_50():
    """Fetch list of people over 50 years of age"""
    if request.method != "GET":
        raise HTTPException(status_code=405, detail="Method Not Allowed")

    over_50 = [p for p in people if p["age"] > 50]

    return {
        "method": "GET",
        "_verb": "get",
        "data": over_50
    }
```

This endpoint adheres to the provided rules and examples:

1. It uses the `@router.get` decorator for the `/people` endpoint.
2. It validates the request method and raises a 405 error if not GET.
3. It filters the `people` list to only include those over 50 years old.
4. The response includes the required `method` and `_verb` fields, as well as the filtered `data`.

Note that this assumes the `people` list is already defined and populated with dictionaries containing `name` and `age` keys.