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How to check a python list to see if 5 sequential items are identical?

I am creating a 15x15 tic tac toe game. One of the conditions is to check if the user has won, which in this case, the user needs to get 5 in a row...whether that be horizontally, diagonally, or vertically. I am having trouble figuring out how to check this. Any help is appreciated, and please stick to the more basic capabilities of Python as I am just starting. My code is below.

class FiveBoard:
    """"""

    def __init__(self):
        """"""
        self._board_list = [
                            ['', '', '', '', '', '', '', '', '', '', '', '', '', '', ''],  # 1
                            ['', '', '', '', '', '', '', '', '', '', '', '', '', '', ''],  # 2
                            ['', '', '', '', '', '', '', '', '', '', '', '', '', '', ''],  # 3
                            ['', '', '', '', '', '', '', '', '', '', '', '', '', '', ''],  # 4
                            ['', '', '', '', '', '', '', '', '', '', '', '', '', '', ''],  # 5
                            ['', '', '', '', '', '', '', '', '', '', '', '', '', '', ''],  # 6
                            ['', '', '', '', '', '', '', '', '', '', '', '', '', '', ''],  # 7
                            ['', '', '', '', '', '', '', '', '', '', '', '', '', '', ''],  # 8
                            ['', '', '', '', '', '', '', '', '', '', '', '', '', '', ''],  # 9
                            ['', '', '', '', '', '', '', '', '', '', '', '', '', '', ''],  # 10
                            ['', '', '', '', '', '', '', '', '', '', '', '', '', '', ''],  # 11
                            ['', '', '', '', '', '', '', '', '', '', '', '', '', '', ''],  # 12
                            ['', '', '', '', '', '', '', '', '', '', '', '', '', '', ''],  # 13
                            ['', '', '', '', '', '', '', '', '', '', '', '', '', '', ''],  # 14
                            ['', '', '', '', '', '', '', '', '', '', '', '', '', '', '']  # 15
                            ]
        self._current_state = "UNFINISHED"

    def get_current_state(self):
        """"""
        return self._current_state

    def print_board(self):
        for row in self._board_list:
            print(row)

    def make_move(self, row, col, mark):
        """"""

        for row in self._board_list:
            for col in row:
                if col == 'x':

                elif col == 'o':


        if self._current_state == "DRAW":
            return False
        if mark == 'o':
            if self._board_list[row][col] == '':
                self._board_list[row][col] = mark
                return True
            else:
                return False
        elif mark == 'x':
            if self._board_list[row][col] == '':
                self._board_list[row][col] = mark
                return True
            else:
                return False
        count = 0
        for row in self._board_list:
            for col in row:
                if col != '':
                    count += 1
        if count == 225:
            self._current_state = "DRAW"




board = FiveBoard()
board.print_board()
print("--------------------------------------------------------------")
board.make_move(0, 14, 'x')
board.print_board()
print("--------------------------------------------------------------")
board.make_move(6, 11, 'x')
board.print_board()
print("--------------------------------------------------------------")

This function will work for you. You just have to take all the horizontal, vertical and diagonal points in separate lists .

The final double for loop just checks for any continuous mark 5 times.

def check_winner(self, row, col, mark):
    board_len = len(self._board_list)

    hor_points = [(row + x, col) if 0 <= row + x < board_len else None for x in range(-4, 4)]
    ver_points = [(row, col + x) if 0 <= col + x < board_len else None for x in range(-4, 4)]
    diag1_points = [(row + x, col + x) if all([0 <= y < board_len for y in [row + x, col + x]]) else None for x in
                    range(-4, 4)]
    diag2_points = [(row + x, col - x) if all([0 <= y < board_len for y in [row + x, col - x]]) else None for x in
                    range(-4, 4)]

    for x in [hor_points, ver_points, diag1_points, diag2_points]:
        count = 0
        for y in x:
            if y and ((self._board_list[y[0]][y[1]] == mark) or (y[0] == row and y[1] == col)):
                count += 1
            else:
                count = 0
            if count == 5:
                return 'WINNER'
    return 'NO WIN'

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