Zakāt is obligatory on wealth that reaches the niṣāb and remains in one’s possession for a lunar year. The Prophet ﷺ established the niṣāb for gold and silver, and these two metals historically served as the basis for monetary wealth. The Prophet ﷺ said: “There is no zakāt on less than twenty dinars of gold.” (Abu Dāwūd), and he said: “There is no zakāt on less than five ounces of silver.” (Bukhari and Muslim).

In classical fiqh, scholars explained that zakatable wealth of the same category should be combined when calculating niṣāb. Gold, silver, and money are considered part of the same general category because modern currency represents monetary value historically linked to gold and silver. For this reason, contemporary scholars generally treat cash, bank balances, gold, and silver as part of the same zakatable pool of wealth.

Therefore, when calculating zakāt, one normally combines all monetary assets, such as cash, bank savings, investment accounts, and gold or silver, when determining whether the niṣāb has been reached. If the combined value exceeds the niṣāb threshold and a lunar year has passed, zakāt is due on the entire zakatable amount.

In the example mentioned, the $100,000 alone already exceeds the niṣāb by a large margin, so zakāt would be due regardless. The 5 grams of gold would simply be included in the total zakatable assets if zakāt is due on that type of jewelry according to the opinion one follows. If someone follows the majority opinion that personal jewelry used for adornment is not zakatable, then that jewelry would not be included. If one follows the Hanafi position that gold jewelry is zakatable, then its value would be added to the total.

The key principle is that wealth serving the function of money is generally combined for zakāt purposes rather than calculated separately in isolation. Separating them only matters when determining whether a particular category itself reaches niṣāb when no other monetary assets exist.

Accordingly, in your example, zakāt would be due because the cash itself already exceeds the niṣāb. Whether the small amount of gold is included depends on whether it is considered zakatable jewelry according to the opinion one follows.