Double exponential decay with values going below the start point of the fitted curve

I have a small dataset with 5 points where x values are log(time) and y = obs. It is known that the behavior is an exponential increase for the first and second (x,y) values and then decreases linearly. The interpolant fit to the data points looks something like shown, but I want to create something like the red curve, which is more meaning full to my data, as it decays slowly and then should become constant. I have tried the double exponential decay function, but it doesn't give me good results, as the first peak becomes too high, close to 170% on the Y scale, which has no physical meaning in my case. The fitted equation: $$y = a*exp(b*x)+c*exp(d*x)$$

I'm not a Maths expert, but I would really appreciate it if you could suggest to me some equations or an improvement in my fit to help me resolve this problem.

The data looks something like this:

X = [0 3.3 4.02 4.71 5.41] Y = [100 111.38 78.64 71.89 66.75]