It depends on what kind of 3 you were at as well.
When you CT, your enthusiasm goes down by half. So if you were at a flat five, you'd go down to 2.5. The game rounds though, so that 2.5 would appear as a 3.
When you TIE, it only increases by 1/3. So, a TIE after a CT could have you as low as a 3.3.
Previously, when you said you went from a 3 to a 5, you could have been at a 3.4, then a TIE would move up to a 4.5, which would display as a 5.