This study aimed to select the best reaction conditions to produce 5-hydroxymethylfurfural (HMF) from cellulose using heterogeneous catalyst based on a heteropolyacid (H₃PW₁₂O₄₀—HPW) and Nb₂O₅. Initially, the influence of the temperature (160 or 200 °C), acetone:water ratio (50:50 or 75:25 v/v), cellulose load (5% or 10% w/v) and catalyst concentration (1% or 5% w/v) on HMF production from cellulose was evaluated through a Taguchi’s L₁₆ screening experimental design. Afterwards, the main variables affecting this process, namely the temperature (160–240 °C) and acetone:water ratio (60:40–90:10 v/v), were optimized using a central composite rotatable design. Next, a kinetic study on HMF production from cellulose was carried out. Finally, HMF production from cellulose obtained from different biomass sources was evaluated. It was found that the reaction conditions able to result in maximum HMF yield, i.e., around 20%, were 200 °C, acetone:water ratio of 75:25 (v/v), 10% w/v of cellulose, and 5% w/v of catalyst concentration. The kinetic study revealed that the Langmuir–Hinshelwood–Hougen–Watson approach fit to the experimental data. Under the optimized conditions, the catalyst HPW/Nb₂O₅ was also effective in converting different sources of cellulose into HMF.