Los Angeles County’s unemployment rate fell to 9.2 percent in December, its lowest point in more than five years, according to state figures released Friday. The rate was down from 9.5 percent in November and well below the 10.3 percent rate of a year ago. But the county’s job creation machine stalled last month as employers only added 1,400 net jobs to their payrolls, according to figures from the state Employment Development Department. The decline in the unemployment rate was driven by more than 30,000 people dropping out of the labor force, likely because they gave up looking for work during the holiday season. The actual number of county residents who reported they were working was unchanged from November with nearly 4 million payroll jobs. In the greater Valley region, Lancaster had the highest unemployment rate at 12.5 percent, down from 13.3 percent in November. Palmdale was second at 11 percent, down from 11.8 percent the previous month. Elsewhere, Glendale had 7.6 percent, down from 8.2 percent in December; Burbank reported 7.1 percent, down from 7.6; and Santa Clarita came in at 5.3 percent, an improvement over 5.7 percent in December. The largest city in the region, Los Angeles, reported unemployment of 9.7 percent in December compared to 10.4 percent the previous month. In the county, the trade, transportation and industry was the top employment generator with 4,900 jobs. The retail trade accounted for most of the growth with 3,700 jobs. Government and professional services added 2,100 jobs and educational and health services gained 1,500. The county unemployment rate of 9.2 percent was higher than the state rate of 8.3 and the national unemployment of 6.7 in December.