Rita bakes pies at a bakery. The number of pies she can bake, $x$, is limited by the ingredients they have in stock. This situation is represented by $2x-3<7$ and $5-x<8$. Solve the compound inequality and write the viable solutions.
$<x<$
Rita can bake or fewer pies.

Step 1 ：The problem is asking for the range of values that $x$ can take, given the two inequalities $2x-3<7$ and $5-x<8$. To find this range, we need to solve each inequality separately and then find the intersection of the two solution sets.

Step 2 ：Solving the first inequality, $2x-3<7$, we get $x<5$.

Step 3 ：Solving the second inequality, $5-x<8$, we get $x>-3$.

Step 4 ：The solution to the compound inequality is the range of values between -3 and 5. However, since the number of pies that Rita can bake cannot be negative, we need to adjust the lower limit to 0.

Step 5 ：So, the solution to the compound inequality is $0\le x\le 5$.

Step 6 ：Final Answer: Rita can bake between 0 and 5 pies, inclusive. So, the solution to the compound inequality is $0\le x\le 5$. In Latex format, the final answer is $\boxed{{\displaystyle 0\le x\le 5}}$.