The $5\text{th}$ term in the following series:
$$a{b}^2+b{c}^2+c{d}^2+\dots \text{ to }25\text{ terms will be:}$$

Let's break down each term of the pattern sequentially to analyze the alphabetical order:
*$1\text{st}$ term:** Uses the $1\text{st}$ letter ('a') and squares the $2\text{nd}$ letter ('b') $⟹a{b}^2$
*$2\text{nd}$ term:** Uses the $2\text{nd}$ letter ('b') and squares the $3\text{rd}$ letter ('c') $⟹b{c}^2$
*$3\text{th}$ term:** Uses the $3\text{rd}$ letter ('c') and squares the $4\text{th}$ letter ('d') $⟹c{d}^2$

Following this consecutive progression:

*$4\text{th}$ term:** Will use the $4\text{th}$ letter ('d') and square the $5\text{th}$ letter ('e') $⟹d{e}^2$
*$5\text{th}$ term:** Will use the $5\text{th}$ letter ('e') and square the $6\text{th}$ letter ('f') $⟹e{f}^2$

Thus, the $5\text{th}$ term is $e{f}^2$.