Question about gordon growth and expected stock prices
Plugging in the numbers into the Gordon's growth formula does not tell what will happen to the price of the house -it just verifies that the numbers given do satisfy the formula.  

To see what will happen to the price in the future, you have to go to the definition of the return on an asset

$$r_{t+1} =  \frac {P_{t+1}+D_{t+1}-P_t}{P_t} = \frac {\Delta P_{t+1}}{P_t} + \frac {D_{t+1}}{P_t} \tag{1}$$

The right-hand side now is clearly "Asset percentage appreciation(Capital Gain) + rate of return on asset value" which is indeed the Total Return on an asset expressed in percentages.  

But we have assumed (and the numbers given verify the initial condition), that Gordon's formula holds so

$$P_t = \frac {D_{t+1}}{r-g} \implies P_t(r-g) = D_{t+1} \tag{2}$$

Substitute $(2)$ into $(1)$ to get

$$r_{t+1} = \frac {\Delta P_{t+1}}{P_t} + \frac {P_t(r-g)}{P_t} = \frac {\Delta P_{t+1}}{P_t} + r-g \tag{3}$$

Now, reasonably we should identify "expected (total) return per period" $r$ with "total return next period" $r_{t+1}$.

Then  $(3)$ becomes

$$r_{t+1} = r = \frac {\Delta P_{t+1}}{P_t} + r-g \implies \frac {\Delta P_{t+1}}{P_t} = g \tag{4}$$

which in our case, means that the value of the house will appreciate $5$% per year. Intuitively, since expected Total Returns are $10$% and what we get out of the house as income ($D_{t+1}/P_t$) is $5$%, the other component of Total Returns, house price appreciation, must cover the distance between the two, which is another $5$%. 

Note: Whether this increase in price refers to "asking" price or "equilibrium" price is another matter that involves a more elaborate modelling of the situation.