\(R_{G}=60 \Omega\)

When the galvanometer is shunted by a resistance \(r\), its effective resistance

\(R_{P}=\frac{R_{G} r}{R_{G}+r}=\frac{60 \times 0.02}{60+0.02} \approx 0.02 \Omega\)

Total resistance of the circuit \(=R+R_{P}=R+0.02\)

Current, \(I=\frac{5}{R+0.02} \Rightarrow 1=\frac{5}{R+0.02}\)

\(R+0.02=5 \Rightarrow R=5-0.02=4.98 \approx 5 \Omega\)