Shenelle has some square tiles. Some of the tiles have side length $5\text{ cm}$ while the others have side length $3\text{ cm}$. The total area that can be covered by the tiles is exactly $2014\text{ cm}^2$. Find the least number of tiles that Shenelle can have.
1. **Formulate the problem as a linear Diophantine equation:**
   Given that the side lengths of the tiles are \(5 \text{ cm}\) and \(3 \text{ cm}\), the areas of these tiles are \(25 \text{ cm}^2\) and \(9 \text{ cm}^2\) respectively. Let \(x\) be the number of \(25 \text{ cm}^2\) tiles and \(y\) be the number of \(9 \text{ cm}^2\) tiles. The total area covered by the tiles is \(2014 \text{ cm}^2\). Therefore, we have the equation:
   \[
   25x + 9y = 2014
   \]

2. **Find an initial solution to the Diophantine equation:**
   We need to find integer solutions to the equation \(25x + 9y = 2014\). We can start by guessing and checking or using the Extended Euclidean Algorithm to find a particular solution. 

   By trial, we find that \(x = 1\) and \(y = 221\) is a solution:
   \[
   25(1) + 9(221) = 25 + 1989 = 2014
   \]

3. **Generate the general solution:**
   The general solution to the linear Diophantine equation \(25x + 9y = 2014\) can be written as:
   \[
   x = x_0 + 9k \quad \text{and} \quad y = y_0 - 25k
   \]
   where \((x_0, y_0)\) is a particular solution and \(k\) is an integer. Using the particular solution \((1, 221)\), we get:
   \[
   x = 1 + 9k \quad \text{and} \quad y = 221 - 25k
   \]

4. **Find the smallest non-negative integer values for \(x\) and \(y\):**
   We need both \(x\) and \(y\) to be non-negative integers. Therefore:
   \[
   1 + 9k \geq 0 \quad \text{and} \quad 221 - 25k \geq 0
   \]
   Solving these inequalities:
   \[
   1 + 9k \geq 0 \implies k \geq -\frac{1}{9} \implies k \geq 0 \quad (\text{since } k \text{ is an integer})
   \]
   \[
   221 - 25k \geq 0 \implies 25k \leq 221 \implies k \leq \frac{221}{25} \implies k \leq 8.84 \implies k \leq 8
   \]

   Therefore, \(k\) can take integer values from \(0\) to \(8\).

5. **Minimize the total number of tiles:**
   We need to minimize \(x + y\):
   \[
   x + y = (1 + 9k) + (221 - 25k) = 222 - 16k
   \]
   To minimize \(x + y\), we maximize \(k\). The maximum value of \(k\) is \(8\):
   \[
   x = 1 + 9(8) = 1 + 72 = 73
   \]
   \[
   y = 221 - 25(8) = 221 - 200 = 21
   \]
   Therefore, the minimum number of tiles is:
   \[
   x + y = 73 + 21 = 94
   \]

The final answer is \(\boxed{94}\)