For particularly important documents I take you back to the covers with reinforced back panel, which it also is, of course a bit more expensive.
Who on the other hand often (larger amounts) of these envelopes needed should consider to look at packaging sizes of 250 envelopes, as they are expected to cover much cheaper.
For up to 5 sheets in my experience the format C4 would be sufficient.
The following is a brief overview of the most common envelope sizes:
Standard size (in my experience, ideal for up to 5 sheets):
DIN C6 = 114 x 162 mm (2 x folded sheet of A4 paper - postcard format)
DIN C5 = 162 x 229 mm (1 x folded sheet of A4 paper)
DIN C4 = 229 x 324 mm (unfolded A4 sheet)
Light oversize (in my experience, ideal for consignments of more than 5 sheets, for example, applications.):
DIN B6 = 125 x 176 mm (2 x folded sheet of A4 paper - postcard format)
B5 = 176 x 250 mm (1 x folded sheet of A4 paper)
B4 = 250 x 353 mm (unfolded A4 sheet)