# joint probability multiple events from single conditional events

I have five independent events $E_1,E_2,E_3,E_4, E_5$, with their conditional probability values for a given outcome.

Eg - $P(Y|E_1), P(Y|E_2), P(Y|E_3), P(Y|E_4), P(Y|E_5)$

Given the above can I find $P(Y|E_1, E_2), P(Y|E_4, E_3, E_5)$? which is basically any combination of the above events given as the condition. It does not have to be exact even an approximation is sufficient.

No.   You need much more information about the series of $\{E_k\}$ events and their relation to $Y$.
For instant, since we have the following, we can see that we cannot express $\mathsf P(Y\mid E_1, E_2)$ in terms of $\mathsf P(Y\mid E_1),\mathsf P(Y\mid E_2)$ with just the given details.
$$\mathsf P(Y\mid E_1, E_2) =\frac{\mathsf P(Y, E_1\mid E_2)}{\mathsf P(E_1\mid E_2)} = \frac{\mathsf P(Y, E_1, E_2)}{\mathsf P(E_1, E_2)}$$