Final answer:
The 10-day VaR is calculated by multiplying the 1-day VaR of $5,000 by the square root of 10, resulting in a 10-day VaR of approximately $15,811.39.
Step-by-step explanation:
The 10-day VaR of a bank's trading portfolio, given a 1-day VaR of $5,000 and assuming that daily earnings are independently and normally distributed, can be estimated using the square root of time rule. According to this rule, the 10-day VaR is found by multiplying the 1-day VaR by the square root of the time horizon. Hence, the 10-day VaR is $5,000 multiplied by the square root of 10, which equals $5,000 * 3.16227766016838 (approximate value). The 10-day VaR would therefore be approximately $15,811.39.