There are 100 new pence in a British pound (GBP) and one British pound is worth $1.60 US dollars at today's exchange rate. (Look up exchange rates at xe.com, they change continuously.) So 5 pence is worth about 8 US cents. All dates are worth the same, 1968 to present, with and without the 'new' annotation.
If you have a completely uncirculated 5 new pence, a collector might be interested in buying it for his or her collection. Most collectors would pay one or two US dollars for a nice looking coin.
Five new pence is worth the same as five pence. In the UK, 'Decimal Day' happened in 1971, when the old system of pence, shillings, and pounds was replaced by the new decimal 100 pence in one pound system. Prior to decimal day there were 240 pence in a pound. The Royal Mint annotated coins worth the new rate as 'new pence' and continued to do so for ten years, until 1981.
The coin in our main picture (upper left) is a 'business strike' new pence coin, meaning it was produced for normal circulation using the new pence rate of 100 pence per pound. The coin in our secondary picture (to the right) is a 'proof' 5 pence coin, meaning it was produced especially for collectors and not for circulation. Since the proof coin is dated after 1981, the 'new' has been dropped. Both 'new pence' and 'regular pence' are worth the same today, but proof coins are often worth more than business strikes. A typical 5 pence proof coin is worth a few US dollars.