I often have the problem that I can get a Cryomancer out or wait a turn or two and get it with +2/+2. Below shows a really stark example:
So, in the example above I have a choice (note that the board is empty and I am playing against a Paladin). I can use all my mana and deploy the Cryomancer immediately, but it will have no buffs and just be +5/+5. Otherwise, I can do nothing except use my hero ability for one damage against the enemy hero and waste 3 mana. However, if I opt for choice 2, then I get to get out the Cryomancer next turn with +2/+2 (for a total of +7/+7) and the Glacial Shard.
In this particular example, I chose to wait. My thinking was that even if the Paladin played a 6-mana minion, I would freeze it for one turn anyway with the Glacial Shard and get out the Cryomancer with +7/+7. So, I just wasted the 5 mana and waited a turn.
Best Answer
There isn't actually one answer for all cases here. You already know what deck you're playing, and by turn five you should have a good idea of the type of deck your opponent is playing (face, tempo, combo, control).
You already have a turn six play in the archmage, so in all matchups except one, you want to play the 5/5 on turn five for the tempo (this statline is only slightly below vanilla stats for a five mana card and totally fine to play tempo).
The only matchup where you would want to wait is control-vs-control where your deck is slower/heavier. In all other cases the tempo from the 5/5 will be much more useful to the coming turns.