If gold was worth $35 and once in 1965 and NASA's budget was $5 billion then and equivalent to about $40 billion in today's money then it is mathematically impossible that today's $26 billion budget with gold priced at $1800/oz is the equivalent value of about 65% of the 1965 budget.
The inflation adjustment numbers must be off by a lot. The proposed 2022 budget is only worth half a billion dollars in 1965 money, but according to the data on the chart, $26 billion in the current era should be worth about $3 billion in 1965 money.