According to http://www.phys.washington.edu/users/ellis/Phys5578/SU3_5.htm or the related Wikipedia article, the following equation should hold:
$[ \frac{\lambda_3}{2}, \frac{\lambda_4}{2}] = i f^{345} \frac{\lambda_5}{2} $
and indeed one can check that $ \frac{\lambda_3}{2} \frac{\lambda_4}{2} - \frac{\lambda_4}{2} \frac{\lambda_3}{2} = i \frac{1}{2} \frac{\lambda_5}{2}$.
However, upon permutation of indices, the equation
$[ \frac{\lambda_4}{2}, \frac{\lambda_5}{2}] = i f^{453} \frac{\lambda_3}{2} $
no longer holds (where I'm assuming $f^{453} = \frac{1}{2}$).
Rather, using the standard Gell-Mann matrices, I get that $[ \frac{\lambda_4}{2}, \frac{\lambda_5}{2}] - i f^{453} \frac{\lambda_3}{2} = \begin{pmatrix} i/4 & 0 & 0 \\ 0 & i/4 & 0 \\ 0 & 0 & -i/2 \end{pmatrix} $
What am I doing wrong?