The 1964 and 1965 Fairlanes have a common platform and rear axle assy. However, the 1965's had a 116.0" w/b and most 64's were 115.5". The 1/2" was gained by relocating the pin in the Rear Spring assy.
My 64 Thunderbolt came with K-H 15 x 7" steel rear wheels with 5" rear spacing. I've run on the one car 15 x 8" Super Tricks with 6" rear spacing on 15x10x29 Goodyear slicks. However, from the factory the Thunderbolt had a section of the rocker panel removed for tire clearance. To take the slicks off I normally raise the car from the track bar crossmember and let some of the air out of the slicks to get them to clear. I think you will find the rocker panel is the limiting factor for tire height. The 65 allows 1" taller tires due to the .5" increase in w/b.
Just a few weeks ago someone asked this same basic question on the FCA Website Forum.
I am pretty sure the 65 isn't any wider in the wheel tub than a 64 but the rocker may be like Dennis says and then you should be able to get a 27" diameter squeezed in there. Width of rim and backspacing is absolutely critical and most older style wheels won't fit. The deep backspace modern car ones will fit the back but not the front. For instance a 17" late 90's Mustang Bullitt wheel or a 16" Probe GT wheel fits perfect out back. Neither fits the front without spacers or narrowing the 8" rim to 7" or less to get the backspace under 4 3/4".
An 8" rim is maximum and that needs around a 6" backspace. You will find most rims have a 3 1/2" to 4 1/2" backspace in that size. A narrowed rear end helps that selection a lot.