Additive for water to increase the viscosity to a value between 5 and 20 cP
You wasn't clear about your purpose to increase viscosity of water (water has viscosity of $\pu{1 mPa\cdot s}$ or $\pu{1 cP}$). However, whatever your reason, xanthan gum would be the materiel you are looking for. Kyoto Electronics has published a note on measurement of viscosity of xanthan gum solution. According to their results (average of 5 tests), 0.1% xanthan gum solution has shown viscosity of $\pu{19.1 cP}$. Five sample averages of 0.2% and 0.3% solutions have given viscosity readings of $\pu{57.54 cP}$ and $\pu{134.6 cP}$.
Accordingly, you can use range of percentages (0.01-0.1%)of xanthan gum to get water viscosity of $\pu{5-20 cP}$. The amount of material to add to water is minimal as you wanted. In addition, Casson plot (shear rate versus shear stress) of 0.1% xanthan gum solution is a straight line. Hence this solution is believed to be a Newtonian solution.