A tensioned solvent printed reinforced vinyl can be used, but cast colored vinyl film will last longer. A rigid substrate with a high grade exterior grade pigmented paint will last even longer (bulletin enamel or, my preference, artist's acrylic paint such a Golden or NovaColor). For best results, a mineral silicate paint (Keim) on a masonry wall (can't tell what your wall is made of from the picture) will have outstanding durability and be the best value (if by "long time" you mean decades).
If painting on the wall is an option, I would choose that over a tensioned flexible vinyl for durability (provided the finish on the surface is suitable). The advantage of tensioned printed media is much lower initial cost and the ability to change it out after 5 years or so when it fades or wears out, or when a new image is desired).
The sample was printed on fexible reinforced vinyl (Outdoor Image) and installed in a BannerGrip® frame. About every 3-4 years we change it out (on the fourth one, about ready to do a new one).