Not even close to true.
US GDP in 1965 was $743.7 billion[0].
NASA's budget peaked in 1964–66 when it consumed roughly 4% of all federal spending. The agency was building up to the first Moon landing and the Apollo program was a top national priority, consuming more than half of NASA's budget and driving NASA's workforce to more than 34,000 employees and 375,000 contractors from industry and academia.
$5 billion is 0.67% of $743.7 billion.