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.

[0] https://countryeconomy.com/gdp/usa?year=1965

[1] https://en.wikipedia.org/wiki/Budget_of_NASA

OK I checked. NASA budget in 1965 was indeed just 60 billion, which is like only 8% of not even GDP but U.S. federal budget. Chump change, shame on you SpaceX for not landing on the Moon yet.