See MM p. 180. How does a Half-Red Dragon Veteran have +5 in Athletics? A CR 5 monster has a proficiency bonus of +3; adding the +3 Strength modifier should yield +6, not +5. The same applies to Perception, which should be +3 and not +2.
No it is not an error
The +2 proficiency bonus has been applied consistently to the half-dragon veteran, to attacks as well as skills. Why is this not an error? Because it is the result of applying the half-dragon template to the CR 3 veteran. A CR 3 creature has a +2 proficiency bonus and the template doesn't change this - it just adds additional features which increase the final CR but do not change the proficiency bonus.
Sure looks like it's wrong.
You're right that a CR 5 creature has a proficiency bonus of +3 (MM p.8), and that the ability modifiers for that creature would imply +6 and +3 athletics and perception modifiers, if the Half-Dragon Veteran is assumed to be proficient in those skills. (And, since the Veteran has those proficiencies--cf. MM p.350--I think it's fair to assume the H-D Veteran has them, too.)
This is an understandable mistake, as they look like a direct copy of that line from the Veteran block (MM. p.350).
This was not corrected in the Monster Manual errata, which does have a whole block devoted to the Half-Dragon. So, in my opinion the argument that "they obviously made a mistake" is a little weaker, since they've gone back and looked at that page and have not changed those modifiers.
Still, I would go with +6 and +3, and have now penciled that into my MM. Thanks =)
NO - it is not a misprint.
You can determine this by the following:
A skill bonus is the sum of a monster’s relevant ability modifier and its proficiency bonus, which is determined by the monster’s challenge rating (as shown in the Proficiency Bonus by Challenge Rating table). Other modifiers might apply.
So, a monster's skills can be subject to special rules per each indivuidual monster.
Also, if you look at the Half-Red Dragon Veteran's (PG.350) skills, you can see that while Athletics is definitely a +5, its wisdom is merely a +2, because its wisdom stat is a +0. This would imply that the monster only has a proficiency bonus of +2, which would play in with only a +5 to athletics, +3 STR and +2 proficiency bonus.
Also, after further reviewing the monster's attacks and their descriptions, you can see that his Longsword attack is a +5 to hit (+3 STR modifier and +2 proficiency) and his Heavy Crossbow attack is a +3 to hit (+1 DEX modifier and +2 proficiency).
With the added fact that there is no correction in the Errata:
Half-Dragon (p. 180). Cut the Saving Throws line and the Parry ability from the stat block. Added the following about challenge rating: “To avoid recalculating the creature’s challenge rating, apply the template only to a creature that meets the optional prerequisite in the Breath Weapon table below. Otherwise, use the guidelines in the Dungeon Master’s Guide to recalculate the rating after you apply the template.”
I'd say it's quite concrete that this is NO misprint whatsoever, and this is actually what the developers intended for this monster.
Yes, it is an error
I was not entirely convinced by any of the other answers (though I'd like to thank you for writing them!), so I decided to do some a more thorough analysis and even go so far as to recalculate the Half-Red Dragon Veteran's CR by following the guidelines on the DMG.
As quite rightly pointed out in @Dale M's answer, the HRDV is the result of a template applied to another monster (the Veteran). This is much more evident in the SRD, in which the stat block for the monster comes after the template (in contrast to the MM, in which it is just a float box). And @Arcemius is also correct in saying the HRDV's proficiency bonus is +2 as it currently stands.
Nevertheless, my conclusion is: the HRDV's proficiency bonus is wrong. This implies its skills and attack roll bonuses should be corrected (by +1).
Why is it wrong?
In the template text we find:
Challenge. To avoid recalculating the creature's challenge rating, apply the template only to a creature that meets the optional prerequisite in the Breath Weapon table below. Otherwise, use the guidelines in the Dungeon Master's Guide to recalculate the rating after you apply the template.
This gives us two methods to determine the HRDV's CR. However, the first one immediately implies the CR should be 3 since the Veteran also has CR 3. Admittedly, the HRDV has a couple of "tweaks" in addition to the Veteran's block, namely plate armor instead of splint (an effective +1 AC) and an additional hit die, though neither of those would justify a whopping increase of two CR points.
Nevertheless, we can see the devs did recalculate the CR in this case to arrive at the CR of 5. By using DMG p. 274–275:
Defensive CR. The monster has 65 HP (CR 1/2), but also damage resistance to fire. The HP must be adjusted by a factor of either 1.5 or 2, depending on the monster's expected CR (DMG p. 277). In our case, the expected CR is 5, so its effective HP is 2 * 65 = 130. This would classify it as a CR 4 monster.
The HRDV's AC is 18, which is 4 points higher than the suggested AC 14 for a CR 4 monster, so we adjust its CR up by 2. The defensive CR is thus 6.
Offensive CR. Because of the breath weapon, the HRDV's damage output must be calculated as an average of the damage it can do in the first three rounds of combat (DMG p. 278). An AoE attack like the breath weapon is assumed to hit two targets, so we have 2 * 24 = 48 damage in the first round, plus 7 + 7 + 6 = 20 damage from two longsword and one shortsword attacks in the two following ones. The average damage output (rounded up) is thus 30, which is compatible with a CR 4 monster.
The attack bonus for a CR 4 monster is +5, which is the same as the HRDV, so no adjustments are necessary. Even if we consider the monster to rely more on effects with saving throws, the save DC difference (14 to 15) does not incur any adjustments either.
The final CR rating for the HRDV should be thus 5, which is indeed consistent with the stat block in the MM. Nevertheless, DMG p. 275 clearly states:
With the final challenge rating, you can determine the monster's proficiency bonus using the Monster Statistics by Challenge Rating table.
So it seems the devs neglected this, and left the HRDV with its previous (inherited from the Veteran stat block, that is) proficiency bonus of +2 instead of correcting it to +3.