In a game, there are several tiles of different colors and scores. Two white tiles are equal to three yellow tiles, a yellow tile equals $5$ red chips, $3$ red tile are equal to $ 8$ black tiles, and a black tile is worth $15$. i) Find the values of all the tiles. ii) Determine in how many ways the tiles can be chosen so that their scores add up to $560$ and there are no more than five tiles of the same color.