Learn Italian: Ammesso che il sinistro sia vero, il danno non è dimostrabile. - Assuming that the claim is true, the damage is not provable.

The phrase ammesso che (assuming that / granted that) introduces a hypothetical assumption. Like many conjunctions that set up a premise or condition, it requires the subjunctive mood. Because the main clause is in the present tense (non è), we use the present subjunctive sia.

Doesn't sinistro usually mean 'left' or 'sinister'? Why is it translated as 'claim' here?

You are right that sinistro commonly translates to 'left' (as in la mano sinistra) or 'sinister'. However, in legal, administrative, and insurance contexts, un sinistro is a specific noun meaning an 'accident', 'incident', or an insurance 'claim'.

Could I use another conjunction like posto che instead of ammesso che?

Yes, you can. Posto che (given that / supposing that) is a very common synonym for ammesso che in this type of sentence. Both introduce a premise and both strictly require the following verb to be in the subjunctive.

How is the adjective dimostrabile formed?

It is built from the verb dimostrare (to show / to prove). By dropping the -are infinitive ending and adding the suffix -abile, it becomes an adjective meaning 'provable' or 'demonstrable'. This works exactly like the English suffix '-able'.