Essayez d'utiliser whereBetween
j'espère que ça marche :
$max_scores_table= DB::table('scores_table')
->select(DB::raw('MAX(score) FROM scores_table as MaxScore'))
->whereBetween('id', array(3,5))
->where('score', 'MaxScore')
->get();
OU :
$max_scores_table= DB::table('scores_table')
->whereBetween('id', array(3,5))
->max('score')
->get();