Not sure about the "then the sum of numb" part, but if you are looking for a single value per name, then this is probably what you are looking for:
Code:
SELECT name
sum(numb)
FROM (
SELECT name,
date,
numb,
row_number() over (partition by name order by date desc) as row_num
FROM your_table
) t
WHERE row_num <= 5
GROUP BY name