Are the coins of more value in the sets or taken out the sets. I am new to this, just trying to learn.In the red book a 1986s penny is worth $5 and the proof set is only $7.
You would be hard pressed to get red book prices for individual coins, but if you took the time to sell each one individually, you could make a little more. You have to decide if listing and shipping five coins would be worth the time of doing so.
What you are seeing is what I call "Dealer nuisance values". Selling a proof set means one sale, one transaction, one cost to the dealer. Selling the coins individually means having to package up five items, find five interested buyers, make five sales/transactions, have five times the paperwork and headache, and probably take five times as long to finally get rid of all of them. All that extra work/headache means I'm going to charge more for the individual items. You see the same thing for the values listed for common coins in mid-grades. Stuff that will wholesale in bulk for just a few cents per item list in the book at way more.
The easiest way to end up with a million dollars selling coins is by starting out with a million five.
And every so often you can find a common proof coin that gets an uncommon grade from a TPGS and becomes worth a fortune to some collectors looking for perfection.
I have a proof set from 1988. I think I paid $8 and I think the current value is $8. I was offered $5 for it at my LCS and politely declined. Individually if you add up all of the values of the coins one by one, it's $23. IMO unless the modern proof set contains a silver coin, or rare variety, it's not worth much. $5 was a fair price. My quarter has toned, and the dime has a strange S MM. At some angles it looks like a small piece is missing, and at others, it's sort of there.
The only place that I have ever heard of people who try to value proof sets coin-by-coin is on tv shopping networks when they want to make the sets that they are selling for 2x what they are worth