If an individual has 10 shares of a company in one Demat account and 5 shares in another, and the company has announced a rights issue in the ratio of 1:15, would they be eligible to exercise the rights?

No, the individual would not be automatically eligible to receive Rights Entitlements (REs) in either account because the entitlements are calculated on a per-Demat account basis, and in both cases, the number of shares held is less than the required minimum for a full share entitlement.