1. The problem is to find the value of $x$ in the equation $$\frac{2x+3}{4} = 5.$$\n\n2. The formula used here is to solve for $x$ by isolating it on one side of the equation. We do this by eliminating the denominator first.\n\n3. Multiply both sides of the equation by 4 to cancel the denominator:\n$$4 \times \frac{2x+3}{4} = 4 \times 5$$\n$$\cancel{4} \times \frac{2x+3}{\cancel{4}} = 20$$\n$$2x + 3 = 20$$\n\n4. Next, subtract 3 from both sides to isolate the term with $x$:\n$$2x + 3 - 3 = 20 - 3$$\n$$2x = 17$$\n\n5. Finally, divide both sides by 2 to solve for $x$:\n$$\frac{2x}{2} = \frac{17}{2}$$\n$$\cancel{2}x / \cancel{2} = \frac{17}{2}$$\n$$x = \frac{17}{2}$$\n\n6. So, the solution is $$x = \frac{17}{2}$$ or 8.5.\n\nThis means that when $x$ is 8.5, the original equation holds true.