Can someone write down the calculation method for the pH values ​​for these 5 protolysis equilibria?

Your example is only detachable if one has given acid constants or has good chemical experience that one can estimate usable.

1. HCO3 ̄ comes from carbonic acid (pK1=6.36, pK2=10.33). It is an ampholyte, so we take the approximation formula pH=1⁄2(pK1+pK2)=8.35
2. HPO3 ̄ comes from phosphoric acid (pK1=2.148, pK2=7.198, pK3=12.319). It is also an ampholyte thus pH=1⁄2(pK2+pK3)=9.76; a more accurate formula gives 9.72
3. acetate comes from acetic acid (pKa=4.75); it is a base because it can no longer release H, i.e. pH=1⁄2(14+pKa+lg(c))=8.88
4. HSO4 ̄ comes from sulfuric acid (pK1≅-3, pK2=2). It looks like an ampholyte, but because of the high strength of the first dissociation stage of the H2 SO4 it is extremely little basic and reacts in dilute solutions only as an acid, namely as a medium strength: pH = −lg(√(√(1⁄4Ka2+Kac)−1⁄2Ka)=1.57
5. Cl ̄ can’t do anything because the hydrochloric acid is very strong: pH=7

This is not entirely true to your predetermined values, but good enough that you can assign it with hangings and worts.