Metathesis and polymerizing of diammonium phosphate or ammonium dihydrogen phosphate and sodium hydroxide (patent: CN1116182),

or

Ammonium phosphate, or mono-ammonium phosphate, or diammonium hydrogen phosphate reaction with sodium hydroxide and phosphoric acid to prepare pentasodium tripolyphosphate by high-temp polymerization and the ammonia gas decomposed from said reaction is absorbed by water to obtain ammonia water, or reacts with different acids to obtain various ammonium salts (CN1132721)

or

By this metathesis process, diammonium hydrogen phosphate or ammonium dihydrogen phosphate and sodium chloride as main raw materials. Its advantages include stable quality, safe production and low cost. (CN1104998). These patents are written in chinese, if you need help in translating the exact recipe, I can help in it.

Furthermore, because there are a hundreds of methods, I suggest going to

www.espacenet.com website, starta search with writing "sodium tripolyphosphate" name into the search window (title and abstract line), and in order to limit the results, the "C01" code into the international classification line. Hundreds of patents will be given and you can select among them the best. If you need further help please do not hesitate to contact with me.

The best way for synthesis sodium tripolyphosphate is by heating a stoichiometric mixture of disodium phosphate and monosodium phosphate under carefully controlled conditions.

2 Na2HPO4 + NaH2PO4 → Na5P3O10 + 2 H2O

Sodium tripolyphosphate is produced by heating a stoichiometric mixture of ,Na2HPO4, and NaH2PO4, under carefully controlled conditions according to the following equation

2 Na2HPO4 + NaH2PO4 → Na5P3O10 + 2 H2O

In this way, approximately 2 million tons are produced annually

The most appropriate one was the following: a 30 wt.% solution of hydrogen peroxide was poured into Erlenmeyer flask. The flask with solution was stirred on magnetic stirrer and cooled up to 0°C, then while stirring the sodium tripolyphosphate (STTP) was added (the amount of the salt was considerably smaller then the amount of peroxide in the solution), incubation period of 40 min followed, after the mixture was poured into another flask, it was cooled up to –15°C and incubated at this temperature for 2 h. The precipitate was filtered and dried in an oven at 50°C in a steam of air. The yield of the product (via STTP) was 68–70%.

i hope this reference will be helpful for you

Chemistry of the Elements - 2nd Edition - Elsevier

https://www.elsevier.com/books/chemistry-of-the-elements/greenwood/978-0-7506-3365-9Write a review. Authors: N. N. Greenwood A. Earnshaw. eBook ISBN: 9780080501093. Paperback ISBN: 9780750633659. Imprint: Butterworth- Heinemann.