A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes?

Let's consider a 5 cm side cube. When we cut 1 cm cubes from it, we effectively create a grid of smaller cubes. 

The number of small cubes that can be cut along one side of the original cube is 5, as each side is 5 cm long, and we cut 1 cm cubes.

Now, the total number of small cubes that can be cut from the original cube is $5\times 5\times 5=125$ small cubes.

Each small cube has 6 faces, and the surface area of one small cube is $1\text{cm}\times 1\text{cm}\times 6=6{\text{cm}}^2$.

So, the total surface area of all the small cubes is $125\text{cubes}\times 6{\text{cm}}^2\mathrm{/}\text{cube}=750{\text{cm}}^2$.

Now, let's compare this with the surface area of the original cube. 

The surface area (S) of a cube is given by the formula:

$\mathrm{S}=6\times (\text{side length}{)}^2$

For the original cube, the surface area is:

${\mathrm{S}}_{\text{original cube}}=6\times (5\text{\hspace{0.17em}cm}{)}^2=6\times 25=150{\text{\hspace{0.17em}cm}}^2$

Therefore, the ratio of the surface areas is:

${\mathrm{S}}_{\text{original cube}}:{\mathrm{S}}_{\text{small cubes}}=150:750$

${\mathbf{S}}_{\mathbf{\text{original cube}}}\mathbf{:}{\mathbf{S}}_{\mathbf{\text{small cubes}}}\mathbf{=}\mathbf{1}\mathbf{:}\mathbf{5}$

So, the required ratio is $\mathbf{1}\mathbf{:}\mathbf{ }\mathbf{5}\mathbf{.}$