import re
from nltk.corpus import stopwords

def find_common_subsequences(sentence, str_list):
    stop_words = set(stopwords.words('english'))
    sentence = sentence.lower()

    str_list = [s.lower() for s in str_list]

    def is_present(subseq, str_list):
        return all(subseq in s for s in str_list)

    def remove_stop_words_and_special_chars(sentence):
        sentence = re.sub(r'[^\w\s]', '', sentence)
        words = sentence.split()
        filtered_words = [word for word in words if word.lower() not in stop_words]
        return " ".join(filtered_words)

    sentence = remove_stop_words_and_special_chars(sentence)
    str_list = [remove_stop_words_and_special_chars(s) for s in str_list]

    words = sentence.split()
    common_grams = []
    added_phrases = set()
    index = 1

    for n in range(5, 0, -1):
        for i in range(len(words) - n + 1):
            subseq = " ".join(words[i:i+n])
            if is_present(subseq, str_list) and not any(subseq in phrase for phrase in added_phrases):
                common_grams.append((index, subseq))
                added_phrases.add(subseq)
                index += 1

    return common_grams