CMM measuring dimensions incorrectly

Lots of unknowns here...

The diameter of the CMM and your manual measure are .005 off, that's a lot.

As stated, check a ring gage.
If the diameter is that far off on the ring, your qualification is shot. Is the "Tool" in the qualification defined correctly (does it list the correct actual diameter of your sphere)? Is the Stylus damaged? Is something attached to the stylus (this happens a lot with scanning and getting material "welded" to the stylus, especially soft material on ruby).

If the diameter matches the ring, why are you so different on the part?
Is there a hole/gouge in the part where the CMM happened to hit?
Is the hole REALLY out of round?
Sheet metal?
Deep drill and you mesured the mouth but the CMM measured in a bulge from a peck cycle?
Reverse taper?

My initial guess is with the qualification of the stylus, and that what you have on there is in trouble somehow (damaged, bent, some crash no one mentioned).
Did you use a "Master" to locate the qualification sphere and then run all used angles? (Another unknown, do you have an articulating head with changeable styli, even?)
When you used the master, did you tell the software that the sphere had moved? (the sphere "moves" when you turn the controller off and then have to home the machine)
When you qualified the styli did you tell the software that the sphere did NOT move? (this is correct, by the way, Yes moved on Master, No moved on all others) (Master is a single stylus and a single head angle, usually A0 B0, it isn't any angle on that stylus, just the one, be the most anal-retentive on this point you can be, and then be worse)

This actually shouldn't give you a bad diameter, unless it is a through hole on a thin part (like sheet metal) and you are actually going under the part or over the part because it is qualified off.
If the qualification is really off, and there is something amiss with the stylus, you could be getting bad alignments and be far off enough you are shallowing out in the hole (with the CMM) and taking hits on the edge break rather than the diameter, even if it isn't sheet metal.

Are the datums good surfaces (flat, intact)?
Where I work now, they bring me parts with datums that hit form better than .002 every single time, and that is large surfaces. holes and small surfaces with form error under .0005.
I've worked where they'd bring me parts with 80% of the datum missing.
Did the CMM maybe hit the datum in a place that was gouged and that's throwing your alignment off so much you are getting garbage results?
Look at the form error of your datums and your circle.

If that is a hole in a block of metal, and the CMM measured the hole .020" deep but you measured .125 deep and the hole isn't square, that can give you different readings on the plate than the CMM.

Definitely start with checking a ring gage and see what the CMM says it is.

Measure a five hit sphere on the qual sphere, rotate the head to a different angle and measure another 5 hit sphere. The X, Y and Z should be very close to identical (manual 5 hits, like .0002 difference per axis).
If they are off by thousandths of an inch, your qualification is bad, requalify.

This is all assuming the program was made correctly in the first place and is currently perfect.

I don't want to start the "how many hits" debate, but if they took a 3-2-1 alignment (and you aren't hitting datum targets) you don't have enough hits, in my opinion. There is zero form error on a three hit plane. At least get 4 or 5 hits so if it isn't flat, you can see it and then know you need to look closer when you get crazy results.

Form will tell you there is an issue and you can run it down. If you take the bare minimum hits so your form is zero, that avenue is lost to you.

Lots of unknowns here...

The diameter of the CMM and your manual measure are .005 off, that's a lot.

As stated, check a ring gage.
If the diameter is that far off on the ring, your qualification is shot. Is the "Tool" in the qualification defined correctly (does it list the correct actual diameter of your sphere)? Is the Stylus damaged? Is something attached to the stylus (this happens a lot with scanning and getting material "welded" to the stylus, especially soft material on ruby).

If the diameter matches the ring, why are you so different on the part?
Is there a hole/gouge in the part where the CMM happened to hit?
Is the hole REALLY out of round?
Sheet metal?
Deep drill and you mesured the mouth but the CMM measured in a bulge from a peck cycle?
Reverse taper?

My initial guess is with the qualification of the stylus, and that what you have on there is in trouble somehow (damaged, bent, some crash no one mentioned).
Did you use a "Master" to locate the qualification sphere and then run all used angles? (Another unknown, do you have an articulating head with changeable styli, even?)
When you used the master, did you tell the software that the sphere had moved? (the sphere "moves" when you turn the controller off and then have to home the machine)
When you qualified the styli did you tell the software that the sphere did NOT move? (this is correct, by the way, Yes moved on Master, No moved on all others) (Master is a single stylus and a single head angle, usually A0 B0, it isn't any angle on that stylus, just the one, be the most anal-retentive on this point you can be, and then be worse)

This actually shouldn't give you a bad diameter, unless it is a through hole on a thin part (like sheet metal) and you are actually going under the part or over the part because it is qualified off.
If the qualification is really off, and there is something amiss with the stylus, you could be getting bad alignments and be far off enough you are shallowing out in the hole (with the CMM) and taking hits on the edge break rather than the diameter, even if it isn't sheet metal.

Are the datums good surfaces (flat, intact)?
Where I work now, they bring me parts with datums that hit form better than .002 every single time, and that is large surfaces. holes and small surfaces with form error under .0005.
I've worked where they'd bring me parts with 80% of the datum missing.
Did the CMM maybe hit the datum in a place that was gouged and that's throwing your alignment off so much you are getting garbage results?
Look at the form error of your datums and your circle.

If that is a hole in a block of metal, and the CMM measured the hole .020" deep but you measured .125 deep and the hole isn't square, that can give you different readings on the plate than the CMM.

Definitely start with checking a ring gage and see what the CMM says it is.

Measure a five hit sphere on the qual sphere, rotate the head to a different angle and measure another 5 hit sphere. The X, Y and Z should be very close to identical (manual 5 hits, like .0002 difference per axis).
If they are off by thousandths of an inch, your qualification is bad, requalify.

This is all assuming the program was made correctly in the first place and is currently perfect.

I don't want to start the "how many hits" debate, but if they took a 3-2-1 alignment (and you aren't hitting datum targets) you don't have enough hits, in my opinion. There is zero form error on a three hit plane. At least get 4 or 5 hits so if it isn't flat, you can see it and then know you need to look closer when you get crazy results.

Form will tell you there is an issue and you can run it down. If you take the bare minimum hits so your form is zero, that avenue is lost to you.