He’s not even close. The following numbers are all from the FBI Uniform Crime Report as reported by the Congressional Research Service.
The US violent crime rate in 1987 was 612.5 and the homicide rate was 8.3. Both peaked in 1991 at 758.2 and 9.8.
These numbers represented significant increases from the 1960s. In 1965 the violent crime rate was 200.2 and the homicide rate was 5.1. However you have to wonder how complete and accurate the crime reporting was in 1965. Still, we’re talking triple the violent crime rate. I was a teenager in the 1960s living in New York City and things were pretty chill. You really didn’t give any thought to wandering all over the city.
Both violent crime and homicide increased significantly after 1965 reaching the peaks mentioned in 1991.
Since the peak in 1991 things have actually been improving. In 2016 the violent crime rate was down to 386.3 and the homicide rate was 5.1. But these represented slight upticks from 2014 when they were 361.6 and 4.4 respectively.
The racial demographics don’t track with these numbers at all. In 1960 it was 88.6% white, 10.5% black and 3.2% Hispanic. Near the crime peak in 1990 it was 80.3% white, 12.1% black and 9.0% Hispanic. But then the crime rate drops and at the last census in 2010 it was 72.4% white, 12.6% black and 16.3% Hispanic.