Discrete Mathematics help

[CanadianAlgebra001]

Let G be a simple graph with 10 vertices such that both G and its complement G are planar.
Show that G must have the following properties:

G has a vertex with degree at least 5.

If X = {v1, v2, v3, v4, v5} is a set of neighbours of a vertex v in G, then the number of edges of G with both ends in X is at most 7.

I am struggling with part 2, i am unsure how to begin

 

[Steven G]

Hi.
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