What happens when you receive a trade token while your inventory is full?

Not long ago, trade tokens were introduced in Clash Royale. You can hold up to 5 of each unique trade token. The trade tokens can be found in the clan war loot bag, or they can be purchased from the shop.

What happens if you have 5 of a trade token and you get another from clan war loot or purchase one from the shop?

Per the wiki article on trade tokens; the last bullet point has the information you are looking for.

If a player already has 10 tokens of a rarity, further tokens received from Special Event Challenges, Global Tournaments, and Clan War Bounties will be converted to Gold (250 for Common, 500 for Rare, 1,000 for Epic and 2,000 for Legendary). Tokens refunded by canceling a trade or purchased in the Shop can surpass the limit without being converted to Gold.