Inheritances are usually a lot harder than this (which is one reason why lawyers and accountants make big bucks).
Ration problems indicate the proportion. Look for a word like "per" when reading ratio problems.
This problem states that the ratio is 5:3:2. That means the first person gets 5 while the second person gets 3 and the third person gets 2. This makes sense, for example if 3 kids get allowances of $5, $3, and $2.
The proportion remains the same when it goes to 10:6:4 and then to 15:9:6. Usually, we reduce the numbers to express them in the smallest integers possible or else in percents (these turn out to be 50%, 30%, 20%). You could write each person' proportion individually as 50/100 = .5 30/100 = .3 and 20/100 = .2.
Now, the problem statement says that the inheritance total is $5,000. The first person gets 50% (half) of the inheritance. That is 0.5*$5000 = 50% of 5000 = $2500
The second person gets 30%, that is 0.3*$5000 = $1500
And the third person gets 20% which is 0.2 * $5000 = $1000.
You're not done yet! You should CHECK your answer. Does $2500 + $1500 + $1000 add up to $5000? YES!
Of course, somebody has to pay the lawyer (or maybe he took his fee out of the estate before $5000 was left).