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We find a parametric solution of an arbitrary symmetric homogeneousdiophantine equation of 5th degree in 6 variables using two primitivesolutions. We then generalize this approach to symmetric forms of any odddegree by proving the following results.  (1) Every symmetric form of odd degree $n\ge 5$ in $6 \cdot 2^{n-5}$variables has a rational parametric solution depending on $2n-8$ parameters.(2) Let $F(x_1, ..., x_N)$ be a symmetric form of odd degree $n\ge 5$ in $N=6\cdot 2^{n-4}$ variables, and let $q$ be any rational number. Then the equation$F(x_i)=q$ has a rational parametric solution depending on $2n-6$ parameters.  The latter result can be viewed as a solution of a problem of Waring type forthis class of forms.

Symmetric homogeneous diophantine equations of odd degree