First, collect your supplies. I like to use paper foundations for log cabins. I have a handy supply of phone books I've been saving. I'm not at all sure they will make them for much longer. Any paper will work, you can sew them without a foundation. In addition to the 5 inch square you will need a variety of strings in both light and dark green. If you can't make the contrast work well enough with just green, you can also use a combination of both dark and neutral. These were all dug out of my string bin which collects any long bits of fabric between 1 and 2 inches in width. Some are straight, but most are angled bits left over from squaring of fabric for rotary cutting.
Traditional log cabins have a center of either yellow or red to represent the fire that was the center of the home. Because we are working in a monochromatic themew, I've chosen to use green instead. Find a roughly square bit of green somewhere between 1.5 and 2 inches to start. You can use a dab of glue stick to hold it in place temporarily or just put it in the middle and hope for the best. Use a somewhat jaunty angle to start the block off feeling "wonky"
Start with a lighter color of fabric and dig for a bit at least as long as the center square. Feel free to roughly cut a size you need from a longer string. Sew with a quarter inch seam.
Press the log open and trim the right edge so that it is even with the center square.
Continuing on with the light colors, find a slightly longer string to fit on the right hand edge. Sew this one down as well.
Press open and trim again, You will continue on with a clockwise rotation.
After two light logs, you will add two dark logs and then repeat until the foundation is covered.
You should get closer and closer to the edges as you continue to add your logs in a clockwise rotation.
When you get closer to the edges, consider using wider or angled strips of fabric. I happened to have some leftover Dresden Plate wedges, but just use whatever you have on hand. The wider strips will just minimize seams along the outside edge.
Keep going until you have completely cover the paper foundation.
Trim your block back to 5 inches unfinished. This will be 4.5 in the framed block. This block will be set straight, showing off the jaunty angle.