Expected ΔE in printed media vs real life

Realistically, how closely can printed media represent real colours?

We recently had paint applied and found the final colour varied from what was expected. While some variation is expected between print and paint, the actual ΔE was >5 across all samples.

Most descriptions of colour differences indicate ΔE of 2 or 3 is enough for any normal person to perceive a different colour, so I don't think a ΔE of 5 can be considered a "slight" variation as the manufacturer claims.

There is nothing wrong with the final paint colour. It is colour matched to another product where it achieves a ΔE of 1.6. The only issue is with how appallingly dissimilar the printed representation is.

CIE-L*ab (D65/10°)CIE-L*ab (D65/10°)