Let A, ɛ > 0 be arbitrary. Suppose that x is a sufficiently large positive number. In this paper we prove that the number of integers n ∈ ( x, x + H ], satisfying some natural conditions, which cannot be represented as the sum of five cubes of primes is ≪ H (log x ) −A , provided that x2/3+ ɛ ≦ H ≦ x .