Nasim can buy 24 cards by buying three 8-packs $(3 imes 8=24)$. Nasim can buy 25 cards by buying five 5-packs $(5 imes 5=25)$. Nasim can buy 26 cards by buying two 5-packs and two 8-packs $(2 imes 5+2 imes 8=26)$. Nasim can buy 28 cards by buying four 5-packs and one 8-pack $(4 imes 5+1 imes 8=28)$. Nasim can buy 29 cards by buying one 5-pack and three 8-packs $(1 imes 5+3 imes 8=29)$. Nasim cannot buy exactly 27 cards, because the number of cards in 8-packs that he buys would be $0,8,16$, or 24, leaving $27,19,11$, or 3 cards to buy in 5-packs. None of these are possible, since none of $27,19,11$, or 3 is a multiple of 5. Therefore, for 5 of the 6 values of $n$, Nasim can buy exactly $n$ cards.