Locally free sheaves of modules form thick subcategory of sheaves of modules

Question

I was wondering, if the following is true: If we have a constant sheaf of rings $K_{X}$ ($K$ a field) over a topological space $X$ and an exact sequence of $K_{X}$-modules

$M_{1}\xrightarrow{f} M_{2}\rightarrow M_{3}\rightarrow M_{4}\xrightarrow{g} M_{5}$

with $M_{i}$ locally free for $i=1,2,4,5$,

then also $M_{3}$ is locally free.