sinken
to fall
To decrease in value, amount, level, or intensity; to become less.
Die Temperaturen sollen in der Nacht unter null Grad sinken.
Temperatures are expected to fall below zero degrees during the night.

to sink / fall
Loading your saved state.
to fall
To decrease in value, amount, level, or intensity; to become less.
Die Temperaturen sollen in der Nacht unter null Grad sinken.
Temperatures are expected to fall below zero degrees during the night.

'Sinken' (to sink/fall) describes a change of state or a downward movement. Therefore, the perfect tense is always formed with the auxiliary verb 'sein' (to be).
Die Preise für Benzin sind letzte Woche stark gesunken.
Gas prices fell sharply last week.
'Sinken' (to sink/fall) is an intransitive verb, which means it does not take an accusative object. The subject of the sentence is the thing or person that goes downward or becomes less on its own.
Die Sonne sinkt langsam am Horizont.
The sun is slowly sinking on the horizon.
In this meaning, 'sinken' (to fall) is often used with abstract values or levels. Typical examples are: die Preise sinken (prices fall), die Temperaturen sinken (temperatures fall), die Arbeitslosigkeit sinkt (unemployment falls), or die Stimmung sinkt (the mood falls).
Im Winter sinken die Temperaturen oft unter den Gefrierpunkt.
In winter, temperatures often fall below freezing.
In its literal meaning, 'sinken' (to sink) is usually used for objects in a liquid, for example 'ein Schiff sinkt' (a ship is sinking). It can also be used figuratively, as in the idiom 'vor Scham im Boden sinken' (to want to sink into the ground from shame).
Der Stein sank sofort auf den Grund des Sees.
The stone immediately sank to the bottom of the lake.
When referring to deterioration, 'sinken' (to decline) is often combined with the reputation, morals, or quality of something.
Das Niveau der Fernsehsendung ist in den letzten Jahren gesunken.
The quality of the TV show has declined in recent years.
to fall
'fallen' and 'sinken' can be very similar when talking about values, amounts, temperatures, or a level. In that case, both mean that something becomes less. In many sentences, you can use both, for example with prices or temperatures. 'fallen' often sounds a bit more direct and works well with numbers that move downward. 'sinken' sometimes sounds a bit calmer or more gradual. Confusing them here is not a big problem, because the meaning often stays the same. Just note: For things in water, 'sinken' is typical; for a fall to the ground, 'fallen' is more typical.

Nach dem Regen sinkt die Temperatur deutlich.
After the rain, the temperature falls noticeably.
Die Mieten fallen in diesem Stadtteil seit einigen Monaten.
Rents in this district have been falling for several months.