Step 1: Place aniline and ammonia.
In aniline $C_6H_5NH_2$, the lone pair on $N$ delocalises into the $\pi$ system of the benzene ring through resonance, reducing its availability for protonation. So aniline is less basic than $NH_3$: $C_6H_5NH_2 < NH_3$.
Step 2: Place benzylamine and ethylamine.
In benzylamine $C_6H_5CH_2NH_2$, the $-CH_2-$ spacer interrupts conjugation, so the lone pair is not delocalised into the ring. Benzylamine is therefore more basic than $NH_3$. Ethylamine $C_2H_5NH_2$ has a stronger $+I$ (electron-donating) effect from the ethyl group than the benzylic carbon, making it more basic than benzylamine. Order so far: $C_6H_5NH_2 < NH_3 < C_6H_5CH_2NH_2 < C_2H_5NH_2$.
Step 3: Place diethylamine at the top.
Diethylamine $(C_2H_5)_2NH$ bears two ethyl groups, each pushing electrons onto $N$ by the $+I$ effect, giving the highest electron density on nitrogen and the strongest basicity. Final order: \[ C_6H_5NH_2 < NH_3 < C_6H_5CH_2NH_2 < C_2H_5NH_2 < (C_2H_5)_2NH \]
\[ \boxed{C_6H_5NH_2 < NH_3 < C_6H_5CH_2NH_2 < C_2H_5NH_2 < (C_2H_5)_2NH} \]