Это можно сделать одним запросом, нужно два объединения:
SELECT t.name,
SUM(IF(f_h.homescore > f_h.awayscore, 1, 0)) AS HomeWins,
SUM(IF(f_h.homescore = f_h.awayscore, 1, 0)) AS HomeDraws,
SUM(IF(f_a.awayscore > f_a.homescore, 1, 0)) AS AwayWins,
SUM(IF(f_a.awayscore = f_a.homescore, 1, 0)) AS AwayDraws
FROM team t
LEFT JOIN fixtures f_h ON f_h.hometeam = t.id AND f_h.id IN (
SELECT id
FROM fixtures
WHERE hometeam = t.id
ORDER BY datetime DESC
LIMIT 5)
LEFT JOIN fixtures f_a ON f_a.awayteam = t.id AND f_a.id IN (
SELECT id
FROM fixtures
WHERE awayteam = t.id
ORDER BY datetime DESC
LIMIT 5)
GROUP BY t.name
Подвыбор необходим для получения только последних 5 приборов.