Hello out there here i am having difficulty in fetching the Brands Per ctegory in the sidebar of my website

Here is the description ..
I am using the feeds and feed uploader to upload feeds and create brands and Product categories in wordpress
The Problem is there is No link Within the Product_category and product_brand and i want too show specific Brands in the
Side bar of a specific category noot the whole brands list which iis going to long down

so i tried out these heavy queries to fetch the brands as per category

but using the INNER JOIN made the databse too slow and the website keeploading without showing brands the query is working fiine the only thing i want to know is to speed up the queries for the Customers so they dont fade up

here are the queries i am using

PHP Code:
$term get_term_by('slug',get_query_var('term'),'product_category');
            
                
        
$q5 "SELECT DISTINCT p1.ID
                FROM
                    
$wpdb->posts p1
                    INNER JOIN 
$wpdb->term_relationships tr1 ON (p1.ID = tr1.object_id)
                    INNER JOIN 
$wpdb->term_taxonomy tt1 ON (tr1.term_taxonomy_id = tt1.term_taxonomy_id)
                WHERE tt1.term_id = '
$term->term_id'
                "
;
            
$q2 "
                SELECT tt2.term_id
                FROM
                    
$wpdb->posts p2
                    INNER JOIN 
$wpdb->term_relationships tr2 ON (p2.ID = tr2.object_id)
                    INNER JOIN 
$wpdb->term_taxonomy tt2 ON (tr2.term_taxonomy_id = tt2.term_taxonomy_id)
                WHERE p2.ID IN (
$q5)
                "
;
            
$q3 "
                SELECT DISTINCT tt3.*
                FROM
                    
$wpdb->posts p3
                    INNER JOIN 
$wpdb->term_relationships tr3 ON (p3.ID = tr3.object_id)
                    INNER JOIN 
$wpdb->term_taxonomy tt3 ON (tr3.term_taxonomy_id = tt3.term_taxonomy_id)
                    INNER JOIN 
$wpdb->terms t3 ON t3.term_id = tt3.term_id
                WHERE 1=1
                    AND tt3.term_id IN (
$q2)
                    AND tt3.taxonomy = 'product_brand'
                ORDER BY t3.name ASC
                "
;
        
$brands $wpdb->get_results($q3); 
The first two queries runs fine but the last one make the datbase query too slow
so any help please