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I am looking for a proof of the following claim:

Given tangential pentagon. Touching point of the incircle and the side of the pentagon,the vertex opposite to that side and the intersection point of diagonals drawn from endpoints of that same side are collinear.

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The GeoGebra applet that demonstrates this claim can be found here.

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This follows from Brianchon's theorem. Note that in order to use that you need to consider the degenerate hexagon, $ABCFDE$. The theorem implies your conclusion.

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