Consider the experiment of drawing two cards from a deck in which all picture cards have been removed and adding their values (with ace = $1$).
What is the sample space?
What is the probability of obtaining a total of $5$ for the two cards?
Let A be the event “total card value is 5 or less.” Find $P ( A )$
Let A be the event “total card value is 5 or less.” Find $P (A^{\complement} )$
Assuming that all face cards are removed, you are left with $52-12=40$ cards.
So, your Sample Space is $40$ cards consisting of all numbered cards (from Ace=$1$ to $10$) in all $4$ suits.
When you draw $2$ cards to obtain a total of $5$, there are following possibilities: $$(4,1),(3,2)$$ and there are $4$ cards of each kind.
So select $1$ of them in $^4C_1$ way, and $2$ cards can be selected from $40$ in $^{40}C_2$ ways. $$P(\text{sum=5})=\frac{^4C_1\cdot ^4C_1+^4C_1\cdot ^4C_1}{^{40}C_2}=\frac{32}{^{40}C_2}$$ For $sum\leq5$, possible cases are: $$(1,1),(1,2),(1,3),(2,2),(1,4),(2,3)$$ There are $^4C_2$ ways to draw $2$ cards with same number, from $4$. $$P(A)=\frac{(^4C_2)+(^4C_1\cdot ^4C_1)+(^4C_1\cdot ^4C_1)+(^4C_2)+(^4C_1\cdot ^4C_1)+(^4C_1\cdot ^4C_1)}{^{40}C_2}=\frac{76}{^{40}C_2}$$ $$P(A^C)=1-P(A)=1-\frac{76}{^{40}C_2}$$