Verified answer

[tex]\displaystyle\bf\\\Big(2-\sqrt{5}\Big)^{2} -2\sqrt{5} \cdot\Big(2-\sqrt{5} \Big)+3=2^{2} -2\cdot 2\cdot \sqrt{5} +(\sqrt{5} )^{2} -2\sqrt{5} \cdot 2+2\sqrt{5} \cdot \sqrt{5} +3=\\\\=4-4\sqrt{5} +5-4\sqrt{5} +10+3=22-8\sqrt{5}[/tex]