You can have ONE and only ONE sf::Texture and assign it to each of 225 sf::Sprite s and then set each Sprite's rectangle.
By doing this:
sf::Texture tiles;
tiles.loadFromFile("Resources/tiles.tga");
sf::Sprite spr(tiles);
spr.setTextureRect(sf::IntRect(0,0,25,25));
Each sprite loaded in memory will be storing the entire tiles.tga image.
EDIT: Just to clarify, the spr sprite in the code above will still be storing the same amount of data on the GPU both BEFORE and AFTER setTextureRect is called.
Could @Laurent please clarify if setTextureRect() frees up the memory of the unused portions of the sprites.