SELECT 
  t.tag_id 
FROM 
  cscart_tags AS t 
  INNER JOIN cscart_tag_links AS tl ON t.tag_id = tl.tag_id 
  INNER JOIN cscart_products AS p ON p.product_id = tl.object_id 
  AND tl.object_type = "P" 
  AND p.status = "A" 
  INNER JOIN cscart_products_categories AS pc ON pc.product_id = p.product_id 
  INNER JOIN cscart_categories AS c ON c.category_id = pc.category_id 
  AND c.status = "A" 
WHERE 
  t.status = "A"

Query time 0.53218

JSON explain

{
  "query_block": {
    "select_id": 1,
    "table": {
      "table_name": "pc",
      "access_type": "index",
      "possible_keys": ["PRIMARY", "pt"],
      "key": "PRIMARY",
      "key_length": "6",
      "used_key_parts": ["category_id", "product_id"],
      "rows": 13336,
      "filtered": 100,
      "using_index": true
    },
    "table": {
      "table_name": "c",
      "access_type": "eq_ref",
      "possible_keys": ["PRIMARY", "p_category_id"],
      "key": "PRIMARY",
      "key_length": "3",
      "used_key_parts": ["category_id"],
      "ref": ["devmotorsbay.pc.category_id"],
      "rows": 1,
      "filtered": 100,
      "attached_condition": "c.`status` = 'A'"
    },
    "table": {
      "table_name": "p",
      "access_type": "eq_ref",
      "possible_keys": ["PRIMARY", "status"],
      "key": "PRIMARY",
      "key_length": "3",
      "used_key_parts": ["product_id"],
      "ref": ["devmotorsbay.pc.product_id"],
      "rows": 1,
      "filtered": 98.3818512,
      "attached_condition": "p.`status` = 'A'"
    },
    "table": {
      "table_name": "tl",
      "access_type": "ref",
      "possible_keys": ["PRIMARY", "tag_id", "ids", "idx_tag_id", "idx_object_id"],
      "key": "PRIMARY",
      "key_length": "6",
      "used_key_parts": ["object_type", "object_id"],
      "ref": ["const", "devmotorsbay.pc.product_id"],
      "rows": 16,
      "filtered": 100,
      "attached_condition": "tl.object_type = 'P'",
      "using_index": true
    },
    "table": {
      "table_name": "t",
      "access_type": "eq_ref",
      "possible_keys": ["PRIMARY", "idx_tag_id"],
      "key": "PRIMARY",
      "key_length": "3",
      "used_key_parts": ["tag_id"],
      "ref": ["devmotorsbay.tl.tag_id"],
      "rows": 1,
      "filtered": 100,
      "attached_condition": "t.`status` = 'A'"
    }
  }
}