Then there exists $n\times n$ matrix $M$ with entries in ${𝔽}_5$ and $b\in {𝔽}_5^n$ such that $\psi (x)=Mx+b$ ($\psi :{𝔽}_5^n\to \widehat{{𝔽}_5^n}$) satisfies $\psi (x)=\varphi (x)$ for ${\mathrm{\Omega }}_{\delta }(|{𝔽}_5^n|)$ elements $x\in S$.