I have a wound which is 1 cm wide and 5 mm deep near my big toe on the left leg. it was cleaned and dressed tightly. will it heal without stitches?

Yes: In clean fresh wounds, we often stitch/suture incision together to minimize scarring. In older dirty wounds, we often leave it open to air (no stitches/sutures) to allow healing from within. This is more likely to cause scarring but we don't want close dirty old wounds out of fear of trapping bacteria in wound. So yes, wounds can heal w/o sutures but will take time & most likely end w/scar.