2.6.5

3 and 5 are prime numbers, so by Lagrange's theorem (or, rather, corollary 6.12) $$H$$ can only contain elements of order 1 and 3, while $$K$$ can only contain elements of order 1 and 5. The only element of order 1 is the identity element 1, therefore $$H \cap K = \{ 1 \}.$$