The least number which when diminished by 5 is divisible by each of 21, 28, 36, 45 is:

Let the required number be $N$. According to the problem statement, $(N-5)$ must be the Least Common Multiple (LCM) of 21, 28, 36, and 45.
Let's find the LCM using prime factorization:

$$21=3\times 7$$

$$28=2^2\times 7$$

$$36=2^2\times 3^2$$

$$45=3^2\times 5$$

$$\text{LCM}=2^2\times 3^2\times 5\times 7=4\times 9\times 5\times 7=1260$$

Since $N-5=1260$:

$$N=1260+5=1265$$