Does anything become incumbent upon the pilgrim if he appoints someone to cast on his behalf during the last days of stoning due to the distance (5 km)?

The basic principle is that whoever is able to stone the Jamarat himself is not permitted to appoint another to stone on his behalf. The pilgrim is obligated to complete the Hajj himself, and for this reason, the Prophet, peace and blessings be upon him, did not allow the weak or the camel herders to appoint proxies for stoning.

However, it is permissible to appoint a proxy for stoning in cases of inability due to a legitimate Sharia-compliant reason, such as illness or weakness that prevents one from enduring the hardship of stoning and crowds, or old age, or a woman's fear for her fetus. The assessment of the state of weakness falls back on the individual concerned and his trustworthiness.