You can make a table. The events are
$S$: Mail is a spam
$cS$: Mails is classified as a spam.
The numbers in the brackets indicate the order of entries.
$$\begin{array}{c|c|c|c} &S & \overline S \\ \hline cS & A(3) & B(5) & C(6) \\ \hline \overline {cS} & (4) & & \\ \hline & 0.005 (1) & 0.995(2) &1 \end{array}$$
... A spam filtering system has a probability of 0.95 to classify correctly a mail as spam.
That means that $0.95=\frac{A}{0.005}\Rightarrow A=...$
and 0.10 probability of giving false positives.
That means a mail is not a spam but it is classified as a spam with a probability of $10\%$:
$\frac{P(\overline S\cap cS)}{P(\overline S)}=\frac{B}{0.995}=0.1$
It is asked for the value of $P(cS)$ which is $A+B=C$
The remaining empty cells can be filled with simplest algebra for further questions.