I've no personal experience of purchasing or using such products but, just in case it helps, I'll point out that envelope sizes are 'C' (rather than 'A') ones. For example C4 envelopes will hold unfolded A4 sheets. So, for your needs, its C5 (rather than A5) envelopes that you're looking for. (The only common exception to that numbering scheme comes from the bizarrely-named DL envelopes, which hold A4 sheets that have been folded into three).
I'll further point out that the Green Stationery Company is a business that you might like to consider purchasing from. They manufacture some of their own products here in the UK, while others are sourced from similarly-minded suppliers within the EU.
https://www.greenstat.co.uk/about-us
Their range of products includes C5 board-backed envelopes:
https://www.greenstat.co.uk/recycled-brown-c5-board-backed-envelopes-pack-10