Is there a way one could say apple cake? Apple cake is not overly common (in the US, at least), but I could see difficulty with lemon pie and lemon cake or chocolate pie and chocolate cake, for instance.
Yes. Cái bánh kem táo. Bánh kem = cream cake. Bánh kem táo = An apple (cream) cake.
The word "bánh" is fairly generic and encompasses all kinds of sweet and savoury cakes, biscuits, cookies, pies, pastries, breads and other snacks.
E.g. Bánh kem = cream cake, bánh mì = bread, bánh mặn = savoury snacks, bánh ngọt = sweet snacks, bánh kẹo = snacks, bánh pie = pie. There are all kinds of Vietnamese bánhs like bánh da lợn/heo = "cow skin cake", bánh in = "print/seal cake" and bánh xèo = "sizzling cake/crêpe/pancake".