A 5-foot wooden gate is not very difficult to make and will fit nicely in a fence gap of around 5 1/3 feet. You can match the height of the gate to the height of the fence, make it a little taller or even have an arched gate top without too much playing around with the design. You don't need expert carpentry skills, and even those with almost no knowledge of woodworking will be able to make their own wooden gate.
Form the 4 planks of 2-by-3 lumber 60 inches in length into a frame. Butt the ends of the side pair against the end pair to make the corners of the frame. Drive two 3-inch nails through the side of each end plank into the ends of the side planks to secure the frame together.
Make a 45-degree cut on each end of a 100-inch plank of 2-by-3 lumber. The cuts should be in opposite directions so that 1 side of the plank is longer than the other. Place this piece of lumber diagonally across the frame. The angled ends will sit flat against the outer edge of the frame. Secure in place as you did the gate frame with 2 1/2 inch nails through the ends of the diagonal plank into the frame.
Lay the frame flat on a work surface, the side with the diagonal plank face down. Evenly space 9 planks of 70-inch-long 1-by-6 lumber vertically over the frame. The 2 outer planks should be flush with the sides of the gate frame; there should be around 2 inches of overhang on each end, with around 1 inch of space between each plank.
Secure the planks in place with 2 1/2-inch nails driven through the tops of the planks into the frame. Your 5-foot-wide gate is ready to hang.
Place 2 T-hinges onto the horizontal planks of the gate frame. Drill pilot holes sized to fit 1-inch galvanised screws through all the screw holes on that half of the hinge. The pilot holes should be a fraction less than the thickness of the screws. Secure the hinge to the gate.
Stand the gate upright between the gateposts. Use pieces of scrap lumber to prop the gate about 2 inches off the ground. The second half of the hinges should sit against the gatepost. Wedge scrap wood in between the gate and the posts so that the gate stays in position without assistance.
Secure the second portion of the hinges to the gateposts as you did the first portion. Remove the pieces of scrap lumber.
Add a door clasp if desired to make the gate lockable. Adjust the height of the gate to suit your needs. To make an arched gate, place all the vertical gate planks together on a work surface and trace the desired arch on 1 end of the planks, then cut the arch with a band or scroll saw. Attach the planks to the gate with the tallest in the middle, grading outward to the shortest on either end. The bottom of all the planks will remain flush.