How can I make a div span multiple rows and columns in a grid?

Keeping your HTML as-is, the layout is not natively possible with flexbox. This is primarily because of the 2 x 2 box occupying the third and fourth columns. The closest you can get is this:

#wrapper{
  display: flex;
  flex-direction: column;
  flex-wrap: wrap;
  align-content: flex-start;
  height: 180px;
  width: 516px;
}
.block {
  width: 90px;
  flex: 0 0 50px;
  margin: 5px;
  background-color: red;
}
.bigger{
  flex-basis: 110px;
}

<div id="wrapper">
  <div class="block"></div>
  <div class="block"></div>
  <div class="block"></div>
  <div class="block bigger"></div>
  <div class="block"></div>
  <div class="block"></div>
  <div class="block bigger"></div>
  <div class="block"></div>
  <div class="block bigger"></div>
  <div class="block"></div>
  <div class="block"></div>
  <div class="block"></div>
</div>

As you can see, the big box is broken up between columns.

As mentioned in the other post you referenced, since you have fixed heights on your child elements (.block), we can determine the height of the container (.wrapper).

By knowing the height of the container, the layout above can be achieved using flex-direction: column and flex-wrap: wrap.

A fixed height on the container serves as a breakpoint, telling flex items where to wrap.

Alternatively, if you can add containers, then the layout is easy. Just create four nested flex containers to hold columns 1, 2, 3-4 and 5, and you're done.

#wrapper {
  display: flex;
  width: 516px;
}

section {
  display: flex;
  flex-direction: column;
}

.block {
  width: 90px;
  height: 50px;
  margin: 5px;
  background-color: red;
}

.bigger {
  flex-basis: 110px;
}

section:nth-child(3) {
  flex-direction: row;
  flex-wrap: wrap;
  flex: 0 0 200px;
}

section:nth-child(3)>.block:last-child {
  flex: 0 0 190px;
  height: 110px;
}

<div id="wrapper">
  <section>
    <div class="block"></div>
    <div class="block"></div>
    <div class="block"></div>
  </section>
  <section>
    <div class="block bigger"></div>
    <div class="block"></div>
  </section>
  <section>
    <div class="block"></div>
    <div class="block"></div>
    <div class="block"></div>
  </section>
  <section>
    <div class="block"></div>
    <div class="block"></div>
    <div class="block"></div>
  </section>
</div>

Otherwise, see this post for more details and other options:

• Is it possible for flex items to align tightly to the items above them?

I understand that you are seeking an answer that doesn't involve HTML Tables or CSS Grid Layout. You mention that you don't want Grid because of weak browser support.

However, around the same time you posted your question, most major browsers released new versions which provide full support for Grid Layout (see details below).

CSS Grid makes your layout simple. There is no need to alter your HTML, add nested containers or set a fixed height on the container (see my flexbox answer on this page).

#wrapper {
  display: grid;                            /* 1 */
  grid-template-columns: repeat(5, 90px);   /* 2 */
  grid-auto-rows: 50px;                     /* 3 */
  grid-gap: 10px;                           /* 4 */
  width: 516px;
}

.tall {
  grid-row: 1 / 3;                          /* 5 */
  grid-column: 2 / 3;                       /* 5 */
}

.wide {
  grid-row: 2 / 4;                          /* 6 */
  grid-column: 3 / 5;                       /* 6 */
}

.block {
  background-color: red;
}

<div id="wrapper">
  <div class="block"></div>
  <div class="block tall"></div>
  <div class="block"></div>
  <div class="block"></div>
  <div class="block"></div>
  <div class="block"></div>
  <div class="block wide"></div>
  <div class="block"></div>
  <div class="block"></div>
  <div class="block"></div>
  <div class="block"></div>
</div>

jsFiddle

How it works:

1. Establish a block-level grid container.
2. The grid-template-columns property sets the width of explicitly defined columns. In this case, the grid is instructed to create a 90px width column, and repeat the process 5 times.
3. The grid-auto-rows property sets the height of automatically generated (implicit) rows. Here each row is 50px tall.
4. The grid-gap property is a shorthand for grid-column-gap and grid-row-gap. This rule sets a 10px gap between grid items. (It doesn't apply to the area between items and the container.)
5. Instruct the .tall item to span from row lines 1 to 3 and column lines 2 to 3.*
6. Instruct the .wide item to span from row lines 2 to 4 and column lines 3 to 5.*

^{* In a five-column grid there are six column lines. In a three-row grid there are four row lines.}

Browser Support for CSS Grid

• Chrome - full support as of March 8, 2017 (version 57)
• Firefox - full support as of March 6, 2017 (version 52)
• Safari - full support as of March 26, 2017 (version 10.1)
• Edge - full support as of October 16, 2017 (version 16)
• IE11 - no support for current spec; supports obsolete version

Here's the complete picture: http://caniuse.com/#search=grid