  We consider the initial value problem of the fifth order modified KdV
equation on the Sobolev spaces. \partial_t u - \partial_x^5u +
c_1\partial_x^3(u^3) + c_2u\partial_x u\partial_x^2 u + c_3uu\partial_x^3 u =0,
u(x,0)= u_0(x) where $ u:R\timesR \to R $ and $c_j$'s are real. We show the
local well-posedness in H^s(R) for s \geq 3/4 via the contraction principle on
$X^{s,b}$ space. Also, we show that the solution map from data to the solutions
fails to be uniformly continuous below $H^{3/4}(R)$. The counter example is
obtained by approximating the fifth order mKdV equation by the cubic NLS
equation.
