WASHINGTON — Consumer spending increased 0.4% in May, a modest gain that suggests Americans remain confident enough about the economy’s outlook to keep shopping.The Commerce Department said Friday that incomes rose 0.5% and inflation remained tame, increasing just 1.5% in the past year. Still, there were signs that core prices, which exclude food and energy, accelerated slightly.Consumer confidence slipped this month but remains at historically high levels. Americans spent more on cars and restaurant meals, according to the government report, a sign that they are willing to make large purchases and spend on discretionary activities, such as eating out.The spending gain in April was revised slightly higher to 0.6%. Consumer spending is closely watched because it drives more than two-thirds of economic activity.Core inflation, which excludes the volatile food and energy categories, rose 1.6% last month, the same as in April. Still, monthly readings have picked up slightly, rising 0.2% for the past two months.Some economists said that suggests that core inflation, which has been slipping this year, may have levelled off and could tick higher in the coming months.