According to the Chicago Manual of Style you are right and it should be "Forty-five-year-old [man]". Quoting from the Chicago Manual of Style (14th edition, page 223):
six year-old girls
man sixty-five years old
child two and a half years old
twenty-four boys five years old
Adjective compounds comprising a number and a unit of measure are hyphenated before a noun. When an adjective is added after the unit of measure, the adjective and unit are joined by a hyphen. When the adjectival compound is preceded by another, modifying number, the hyphenated compound is kept separate from that number. if the compound comes after the noun, it may usually be left open, but in that case the unit is plural if the number is greater than one.
On the internet I have found this page to sum it up:
Hyphenate ages when they are adjective phrases involving a unit of measurement: “Her ten-year-old car is beginning to give her trouble.” A girl can be a “ten-year-old” (“child” is implied). But there are no hyphens in such an adjectival phrase as “Her car is ten years old.”