Let me outline the answer previously given by eyesun:

In order to figure out how something might react with water, it is helpful to describe and categorize the starting material and to find analogies.

1. Apparently, $\ce{P2O5}$ is a group 15 oxide, the oxide of a non-metal.
2. Other non-metal oxides that come to our mind are from the same element ($\ce{P2O3}$), from the same group ($\ce{N2O5}$), or from the neighboring group 14 ($\ce{CO2}$) and group 16 ($\ce{SO2}$, $\ce{SO3}$, $\ce{SeO2}$).

What other compounds do we know that are similar to these oxides?

3. We do know that a number of oxo acids exist. Mostly, they do contain one atom of a group 14-16 element with a couple of oxygen atoms and some protons attached.

4. Can we match these?

$$\ce{H2SO3 <=> SO2 + H2O}$$ $$\ce{H2SO4 <=> SO3 + H2O}$$ $$\ce{H2CO3 <=> CO2 + H2O}$$ $$\ce{2HNO3 <=> N2O5 + 2H2O}$$

We conclude that these non-metal oxides are like oxo acid minus water and we therefore decide to call them anhydrides.

5. Having worked our way through all of these, we decide to apply our knowledge to $\ce{P2O5}$:

$$\ce{2 H3PO4 <=> P2O5 + 2 H2O}$$

to realize that phosphorous pentoxide is the anhydride of orthophosphoric acid.

Let me outline the answer previously given by eyesun:

In order to figure out how something might react with water, it is helpful to describe and categorize the starting material and to find analogies.

1. Apparently, $\ce{P2O5}$ is a group 15 oxide, the oxide of a non-metal.
2. Other non-metal oxides that come to our mind are from the same element ($\ce{P2O3}$), from the same group ($\ce{N2O5}$), or from the neighboring group 14 ($\ce{CO2}$) and group 16 ($\ce{SO2}$, $\ce{SO3}$, $\ce{SeO2}$).

What other compounds do we know that are similar to these oxides?

3. We do know that a number of oxo acids exist. Mostly, they do contain one atom of a group 14-16 element with a couple of oxygen atoms and some protons attached.

4. Can we match these?

   $$\ce{H2SO3 <=> SO2 + H2O}$$ $$\ce{H2SO4 <=> SO3 + H2O}$$ $$\ce{H2CO3 <=> CO2 + H2O}$$ $$\ce{2HNO3 <=> N2O5 + 2H2O}$$

We conclude that these non-metal oxides are like oxo acid minus water and we therefore decide to call them anhydrides.

5. Having worked our way through all of these, we decide to apply our knowledge to $\ce{P2O5}$:

   $$\ce{2 H3PO4 <=> P2O5 + 2 H2O}$$

to realize that phosphorous pentoxide is the anhydride of orthophosphoric acid.

Let me outline the answer previously given by eyesun:

In order to figure out how something might react with water, it is helpful to describe and categorize the starting material and to find analogies.

1. Apparently, $\ce{P2O5}$ is a group 15 oxide, the oxide of a non-metal.
2. Other non-metal oxides that come to our mind are from the same element ($\ce{P2O3}$), from the same group ($\ce{N2O5}$), or from the neighboring group 14 ($\ce{CO2}$) and group 16 ($\ce{SO2}$, $\ce{SO3}$, $\ce{SeO2}$).

What other compounds do we know that are similar to these oxides?

3. We do know that a number of oxo acids exist. Mostly, they do contain one atom of a group 14-16 element with a couple of oxygen atoms and some protons attached.

4. Can we match these?

$$\ce{H2SO3 <=> SO2 + H2O}$$ $$\ce{H2SO4 <=> SO3 + H2O}$$ $$\ce{H2CO3 <=> CO2 + H2O}$$ $$\ce{2HNO3 <=> N2O5 + 2H2O}$$

We conclude that these non-metal oxides are like oxo acid minus water and we therefore decide to call them anhydrides.

5. Having worked our way through all of these, we decide to apply our knowledge to $\ce{P2O5}$:

$$\ce{2 H3PO4 <=> P2O5 + 2 H2O}$$

to realize that phosphorous pentoxide is the anhydride of phosphoric acid.

Let me outline the answer previously given by eyesun:

In order to figure out how something might react with water, it is helpful to describe and categorize the starting material and to find analogies.

1. Apparently, $\ce{P2O5}$ is a group 15 oxide, the oxide of a non-metal.
2. Other non-metal oxides that come to our mind are from the same element ($\ce{P2O3}$), from the same group ($\ce{N2O5}$), or from the neighboring group 14 ($\ce{CO2}$) and group 16 ($\ce{SO2}$, $\ce{SO3}$, $\ce{SeO2}$).

What other compounds do we know that are similar to these oxides?

3. We do know that a number of oxo acids exist. Mostly, they do contain one atom of a group 14-16 element with a couple of oxygen atoms and some protons attached.

4. Can we match these?

$$\ce{H2SO3 <=> SO2 + H2O}$$ $$\ce{H2SO4 <=> SO3 + H2O}$$ $$\ce{H2CO3 <=> CO2 + H2O}$$ $$\ce{2HNO3 <=> N2O5 + 2H2O}$$

We conclude that these non-metal oxides are like oxo acid minus water and we therefore decide to call them anhydrides.

5. Having worked our way through all of these, we decide to apply our knowledge to $\ce{P2O5}$:

$$\ce{2 H3PO4 <=> P2O5 + 2 H2O}$$

to realize that phosphorous pentoxide is the anhydride of orthophosphoric acid.