Separable differentiable equation solution method

I'm stuck on this problem. I don't want it solved for me, but, I don't know where to go further with this.
GIVEN
du/dt=e^(2u+7t)
u(0)=5

REQUIRED
u=?

SOLUTION
to start, I integrated both sides
u=(1/2)e^(7t+2u)+C

used initial condition to solve for C
5=(1/2)e^(10)+C
C=5-(1/2)e^10

plugged C back into integrated formula

u=(1/2)e^(7t+2u)+5-(1/2)e^10

I'm having a problem with the 2u in the exponent. I need an explicit solution and I don't know how to get there. Webwork won't let me submit an answer with "u" in it. What am I supposed to do?

You cannot integrate the both sides directly since u is a function of t.

du/dt = e^(2u+7t)

e^(-2u) du = e^(7t) dt

Now integrate both sides.

(-1/2) e^(-2u) = (1/7) e^(7t) + C

Apply the BC,

(-1/2) e^(-2(u-5)) = (1/7) e^(7t).

Solve for u and you get the answer.

e^(2u+7t) = (e^2u)*(e^7t)
du/dt = e^(2u+7t)
-->
du/dt = (e^2u)*(e^7t)
-->
[e^(-2u)]du = (e^7t)dt
Integrating both sides you get
(-1/2)e^(-2u) = (1/7)e^(7t) + C

" solution is terrible to start "...you have du / dt = e^( 2u ) e^( 7t ) , separate and work