If a $10,000 investment earns a 7% annual return, what should its value be after 5 years?

I think you got a bit muddled there Tetration.  

$$\\FV=10000(1+0.07)^5\\
FV=10000(1.07)^5\\$$

$${\mathtt{10\,000}}{\mathtt{\,\times\,}}{{\mathtt{1.07}}}^{{\mathtt{5}}} = {\mathtt{14\,025.517\: \!307}}$$

$14,025.51

If it has an annual return of 7% it increases with 0.07 times the last year's investment. That means that the total amount of money one year later is 1.07 times the original amount of money.

After one year, the total amount of money is:

10⁴ * 1,07 = 1.07 * 10⁴

After two years, the total amount of money is:

10⁴ * 1,07 * 1.07 = 10⁴ * 1,07² = ...

After three years:

10⁴ * 1,07 * 1.07 * 1.07 = 10⁴ * 1,07³ = ...

Indeed, after x years, the total amount of money, T(x), has grown to:

T(x) = 10⁴ * 1.07^x