Let f be a positive definite integral quinary quadratic form and let r(n, f) be the number of representations of an integer n by f. A quinary quadratic form f is said to be a Bell quinary quadratic form if f is isometric to x_1^2 + 2^α x_2^2 + 2^β x_3^2 + 2^γ x_4^2 + 2^δ x_5^2 for some nonnegative integers α, β, γ, δ. In this talk, we will compute r(n, f) by using the number of representations of the sum of 5 squares for any Bell quinary quadratic form f with class number 2. This is a joint work with Ick Sun Eum.