I guess it is, you can do an EXLPAIN query on it in your MySQL client to see what’s the heavy part of the query and if indexes will help here. Just run the same query and put the syntax EXPLAIN in front of it.
EXPLAIN SELECT t.*, tt.*, tr.object_id FROM wp_terms AS t INNER JOIN wp_term_taxonomy AS tt ON t.term_id = tt.term_id INNER JOIN wp_term_relationships AS tr ON tr.term_taxonomy_id = tt.term_taxonomy_id WHERE tt.taxonomy IN ('genre', 'region', 'publisher', 'language', 'release-year') AND tr.object_id IN (39000) ORDER BY t.name ASC;