Lots of really solid advice already given and good perspectives. This is my advice for what it is worth:
A5o in early position for me is almost always a "no go" unless i am to be BB next hand and only have about 3bb anyhow - kind of leaves me with no choice. Anyhow - also really depends on the players at your table and how they are playing their game....
Last night i "cashed" in two of the step 1 Venom
freerolls and one the
hands that set me up to do it was 33's - my table was fairly tight aggressive so i was in the BB with my pocket 3s sittin on about 14bb's and mp raises, the button jams and had me covered - our original raiser only has about 12bb's or so and has went to showdown with alot of big ace's as well as our dealer...both of them playing the top of their range so heavily - i decided i hope they are holding each others outs and this is my chance - i let it fly and sure enough AQo vs AKo vs my little 33s - board runs out safely, i scoop a nice pot late in the tourni and am able to make a deep run from there to finish 5th overall when the 113 player pool mark was reached.
Anyhow, hope that example was helpful. For me I would much rather be shoving 89s - 55 - A10o + from early position. A5 suited is definitely a push for me from early - its good strategy to call with a big stack from the BB with marginal mediocre hands because people in a "short stack" position will definitely shove light and its worth the risk. If i am 50bb deep and you shove 8 or less into me with blinds being high and antes involved - i will snap call you with 10 8 off and 9 10off - hell sometimes something as loose as K3 suited - again depends on the player and depends on stack sizing, etc. But looking at it, A8s vs 9To is still a 60/40 hand so its not a terrible spot to be in for the bigger stack.
In summary - for myself - when i am short and in a bad spot i try to shove what makes me feel like i have the best chance with instead of what push-fold strategy
tells me to. Id much rather shove 56 offsuit into a table of tighter players just hoping if i get called, that my cards are live and i stand a much less like chance of being dominated with cards that are not so strong. A5 could easily be dominated at a TAG table as well as most other Ax combos below AJ.
Anyways, thats my take on the situation. Was your shove a bad move? Maybe, maybe not - depends on your table and how you felt. At the end of the day the point of this game to make you a winning player is to get your money in good - long term results will be good. You got your stack in good even though you were at risk - cant ask for much more than that. He couldve called you with A7 off and had you in very bad shape. For me, i think even though you got knocked out - you should try and be proud A5 was good there preflop. Keep grinding and keep your head up.