I liked Diana. I think she got a raw deal. She is special to me, and to many, many people. Her likeness appears on British 5 pound coins dated 1999. Other 5 pound coins minted after 1990 appear in many different designs and in three different compositions: copper-nickel, silver, and gold.
The value of these coins, like all modern commemoratives, is exactly aligned with the price of the precious metal they contain. You can add a small amount, a very small amount, for subjective factors such as artistic beauty and sentimental value, but coin dealers are a pretty objective bunch and they won't buy coins for sentimental reasons.
To evaluate the actual (non-sentimental) value of 5 pound coins, start by evaluating their precious metal content:
copper-nickel: no precious metal
silver: 0.841 troy ounces silver
gold: 1.178 troy ounces gold
At today's prices of $1716 and $32.50 US dollars per troy ounce of gold and silver, respectively (look up these prices on kitco.com, they change every day), that's 0.841 x 32.50 = $27 silver value and 1.178 x 1716 = $2021 gold value.
To add value for these coins over and above their precious metal content, consider:
copper-nickel: the coin is worth face value, five pounds, about $8 US dollars
silver: add $10 to the silver value if you are buying it, subtract $10 if you are selling it to a coin dealer
gold: add $200 to the gold value if you are buying it, subtract $200 if you are selling it to a coin dealer
As always on CoinQuest, these are very approximate values. You may be able to do better, or you might not be able to do as well.