Regarding the expected value, what's the meaning of E(-5X) and E(X+Y)? if  X∼N(2,1) then the expected value of −5X ? E(−5X) = -5E(X)
if Y~N=(4,1) then the expected value of X+Y? E(X+Y)=E(X)+E(Y)
Can you please tell me what is the meaning of multiplying or summing expected values ? 
 A: Assume you roll the dice, if you roll a one you win one euro, if you roll a two then you win 2 euro, ... if you roll six than you win six euro.  
If the dice is fair then the probability to roll a one is 1/6, the same for rolling a two, ... the same for rolling a six. 
So for a dice we have $P(X=1)=P(X=2)=\dots = P(X=6)=1/6$. If you get one euro if you throw 1, two euro if you get two, ... then your ''expected win'' is $1 \times 1/6 + 2 \times 1/6 + \dots + 6 \times 1/6=3.5$ which is the expected value of $1X$, i.e. E(1X)=E(X)=3.5$, one because you get 1 euro for each dot that comes up. 
If you get 1000 euro for each dot that comes up, then you have to compute the expected values of $1000X$ to compute your expected profit, i.e. $E(1000X)=1000E(X)=3500$. 
For sums it is simular, but you use two dice, one with an outcome X, the other one with an outcome Y. 
A: To understand the meaning of E(-5X), I used the following R code:
r=rnorm(100,5,5)
library(sm)
d=data.frame(r,-5*r)
colnames(d)=c('newr','oldr')

library(tidyr)
do=gather(d)

sm.density.compare(do[,2],as.factor(do[,1]))

abline(v=5)
text(28,.06,'old center')

abline(v=-25)
text(-50,.06,'new center')
#new mean        
mean(-5*r)


To understand E(X+Y), I used the following R code:
dist1=rnorm(100,5,5)
dist2=rnorm(100,4,4)
#expected value of E(X+Y)=E(X)+E(Y)=5+4=9
XplusY=dist1+dist2
d=data.frame(dist1,dist2,XplusY)
colnames(d)=c('dist1','dist2','newdist')

library(tidyr)
do=gather(d)
sm.density.compare(do[,2],as.factor(do[,1]))

abline(v=9) #the center of multiplying values of two dists
mean(XplusY)  #approximately 9


