Though it may seem strange (probably part of a polynomial trend analysis), you are considering the following contrast for a follow-up test for a 1-way ANOVA with 6 groups: $\displaystyle \psi_{{1}}:$  $\displaystyle {5}\cdot\mu_{{{1}}}-{5}\cdot\mu_{{{2}}}-{7}\cdot\mu_{{{3}}}+{c}_{{{4}}}\cdot\mu_{{{4}}}+{7}\cdot\mu_{{{5}}}+{4}\cdot\mu_{{{6}}}={0}$

Assuming a balanced design, what must the missing coefficient be for this to be a legitimate contrast?
$\displaystyle {c}_{{4}}=$