If total liabilities increased by $25,000 and stockholders' equity decreased by $5,000 during a period of time, then total assets must change by what amount and direction during that same period?

Equity (Owner's Funds) = Assets (-) Liabilities

Thereby,

Assets = Equity (+) Liabilities 

So, now we are going to find the effect of decrease or increase in total assets by using the above mentioned equation.

As per the facts of the question, it is stated that 

Stock holder's equity has decreased by $ 5,000 i.e., reduction (-).

Thereby,

Aggregate effect on Equity and liability side =

((-) $5,000) + (+ $ 25,000) = + $20,000

The aggregate effect of Equity and liability side results into net increase of $20,000.

Thereby, as per the initial phase of discussion 

Assets = Equity + liabilities, which results into

Increase/Decrease in (Equity + Liabilities) = Increase/Decrease in Assets 

Increase of $ 20,000 = Increase of $ 20,000 in Total Assets.

Therefore, the total assets must change by $20,000 and it should be increased

i.e., Option D = $20,000 Increase

Answer is completed.

For refernce, extract of balance sheet is attached below:

Equity and Liabilites: 

Equity

Decrease by $5,000       = (5,000)

Total Liabilities 

Increase by $25,000      = 25,000

Total increase in Equity and Liability = $ 20,000

Assets

since Total equity and liability  have increased by $20,000 the increase in total assets will be arrived as balancing figure and it is increase of $ 20,000.