LOS ANGELES — After nearly five years of brutal economic decline, government retrenchment and a widespread loss of confidence in its future, California is showing the first signs of a rebound. There is evidence of job growth, economic stability, a resurgent housing market and rising spirits in a state that was among the worst hit by the recession.

California reported a 10.1 percent unemployment rate last month, down from 11.5 percent in October 2011 and the lowest since February 2009. In September, California had its biggest month-to-month drop in unemployment in the 36 years the state has collected statistics, from 10.6 percent to 10.2 percent, though the state still has the third-highest jobless rate in the nation.

The housing market, whose collapse in a storm of foreclosures helped worsen the economic decline, has snapped back in many, though not all, parts of the state. Houses are sitting on the market for a shorter time and selling at higher prices, and new home construction is rising. Home sales rose 25 percent in Southern California in October compared with a year earlier.

After years of spending cuts and annual state budget deficits larger than the entire budgets of some states, this month the independent California Legislative Analyst’s Office projected a deficit for next year of $1.9 billion — down from $25 billion at one point — and said California might post a $1 billion surplus in 2014, even accounting for the tendency of these projections to vary markedly from year to year.