Clock

The angular movement speed per second of the erroneous watch is $\dfrac{3\times 60 + 5}{3 \times 60} = \dfrac{185}{180}$ .

The number of seconds the watch has moved from $7:00$ to $16:15$ is:

$N = 16:15-7:00 = 9:15 = (9\times 60+15)\times 60 = 555\times 60$

The actual time has lapsed:

$T = \dfrac {N}{\frac{185}{180}} = \dfrac {555\times 60 \times 180}{185} = 3 \times 60 \times 180 = 9 \times 60 \times 60 = 9$ hours.

The actual time is $7:00+9:00 = 16:00$ or $\boxed{4:00 \text{ pm}}$

Time from 7 am to 4.15 pm = 9 hours 15 minutes = 9 + 1/4 hours=37/4 hours

3 minute 5 seconds of the given clock = 3 minutes of a normal clock

⇒3×1/12 minutes of the given clock = 3 minutes of a normal clock

⇒37/12 minutes of the given clock = 3 minutes of a normal clock

⇒37/720 hours of the given clock = 3/60 hours of a normal clock

⇒37/720 hours of the given clock = 1/20 hours of a normal clock

⇒37/4 hours of the given clock = 1/20×720/37×37/4 hours of the given clock

= 9 hours of the given clock

Hence the correct time = 9 hours after 7 am = 4 pm