If the Japanese price level rises by 5% relative to the price level in the United States, what does the theory of purchasing power parity predict will happen to the value of the Japanese yen in terms of dollars?

According to purchasing power parity theory the trade rates between two monetary standards conform to reflect changes in value level of two nations

Let's consider the exchange rate is $\$1=110yen$

suppose a pen costs $\$1$in us then as per purchasing power parity the same pen costs 110 yen in japan.

if the price increases by 5%, i.e., to 115.5 yen $(110+5\mathrm{\%})$then to attain equilibrium the exchange rate falls to $1=115.5 yen or 5 %

so according to this theory value of Yen will depreciate or fall 5 % in terms of dollars.

Hypothesis of PPP predicts that worth of Yen will devalue against the US dollar. The devaluation in the worth of Yen will be $5\%$against the US dollar, according to the PPP. Therefore, generally more yen, will be utilized to trade 1 USD.