The unstable intersection asserts that any two maps from compacta $X$ and $Y$ to an $n$-dimensional Euclidian space can be arbitrarily closely approximated by maps with disjoint images if and only if the product of $X$ and $Y$ is of dimension at most $n-1$. This conjecture is proved in all the dimensions except $n=5$. We are planning to present the proof for $n>5$. The proof heavily relies on Cohomological dimension and Extension theory and in the first talk we will focus on auxiliary results.