#### Answer

$a^{5}+5a^{4}b^{}+10a^{3}b^{2}+10a^{2}b^{3}+5a^{}b^{4}+b^{5}$

#### Work Step by Step

$(a+b)^{5}$
To find the expansion of the given expression using Pascal's Triangle, use the coefficients in the 6th row, which are: $1, 5, 10, 10, 5, 1$.
Use these coefficients and write descending degrees (exponents) for $a$ and ascending degrees (exponent for $b$ to obtain:
$(a+b)^5=a^{5}+5a^{4}b^{}+10a^{3}b^{2}+10a^{2}b^{3}+5a^{}b^{4}+b^{5}$