1. Find the degree of unsaturation

For $\mathrm{C_5H_{10}}$,

$\text{IHD} = \frac{2C+2-H}{2} = \frac{2(5)+2-10}{2} = \frac{12-10}{2} = 1$

So the compound has one degree of unsaturation.

Since the question asks for cyclic isomers, this one unsaturation must be due to one ring only.

2. List all possible cyclic structural isomers of $\mathrm{C_5H_{10}}$

We need all cycloalkanes with 5 carbons total.

Possible ring skeletons:

(i) Five-membered ring

• Cyclopentane

Count = 1

(ii) Four-membered ring + one carbon substituent

• Methylcyclobutane

Count = 1

(iii) Three-membered ring + two extra carbons

Two possibilities:

• Ethylcyclopropane
• Dimethylcyclopropane

Now for dimethylcyclopropane, distinct positional possibilities are:

• 1,1-Dimethylcyclopropane
• 1,2-Dimethylcyclopropane

(There is no separate 1,3-form in cyclopropane because of symmetry; it is equivalent to 1,2-.)

So under this case, count = 3.

Thus total structural isomers:

$1+1+3=5$

These are:

1. Cyclopentane
2. Methylcyclobutane
3. Ethylcyclopropane
4. 1,1-Dimethylcyclopropane
5. 1,2-Dimethylcyclopropane

3. Now include stereoisomers

Among the above, only 1,2-dimethylcyclopropane shows geometrical isomerism.

Check each structure:

• Cyclopentane: no stereoisomer
• Methylcyclobutane: no stereoisomer
• Ethylcyclopropane: no stereoisomer
• 1,1-Dimethylcyclopropane: no cis/trans possible since both substituents are on same carbon
• 1,2-Dimethylcyclopropane: has cis and trans forms

For 1,2-dimethylcyclopropane:

• cis-1,2-dimethylcyclopropane: one form
• trans-1,2-dimethylcyclopropane: exists as a pair of enantiomers

So this contributes:

$1\text{ (cis)} + 2\text{ (trans enantiomers)} = 3$

Instead of counting it as just one structural isomer, counting all stereoisomers gives 3 forms.

4. Total cyclic structural + stereoisomers

Other four structures contribute one each:

$4$

And $1,2$-dimethylcyclopropane contributes:

$3$

Therefore,

$4+3=7$

5. Final answer

The total number of cyclic structural as well as stereoisomers for $\mathrm{C_5H_{10}}$ is

$\boxed{7}$

6. Comparison with stored correct answer

Stored correct answer = $7$

Our derived answer = $7$

So they agree.