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 linear equations by isolating the variable $x$.\n\n3. First, multiply both sides of the equation by 4 to eliminate the denominator:\n$$4 \times \frac{2x+3}{4} = 4 \times 5$$\nwhich simplifies to\n$$2x + 3 = 20.$$\n\n4. Next, subtract 3 from both sides to isolate the term with $x$:\n$$2x + 3 - 3 = 20 - 3$$\nwhich simplifies to\n$$2x = 17.$$\n\n5. Finally, divide both sides by 2 to solve for $x$:\n$$x = \frac{17}{2} = 8.5.$$\n\n6. Therefore, the solution is $x = 8.5$.