For the following block design I am trying to determine if the design is a BIBD and if so, determine its parameters $v, b ,r, k,$ and $\lambda$. $$V = \{a, b, c, d, e\}$$ blocks: $\{a,b,c,d\}, \{a,c,d,e\}, \{a,b,d,e\}, \{ a,b,c,e\}, \{ b,c,d,e\}$
Relevant formulas: $bk=vr$ and $\lambda(v-1)=r(k-1)$
the parameter $k$ represents the number of elements in each block, so clearly $k = 4$
But how do I proceed to find the other parameters? And is this even a BIBD?