I'll repeat the text of the relevant rules here:
If the spell is on your class’s spell list, you can read the scroll and cast its spell without providing any material components.
If the spell is on your class's spell list but of a higher level than you can normally cast, you must make an ability check using your spellcasting ability to determine whether you cast it successfully.
So, there are two requirements to cast the spell without making the check.
1 The spell is on your class spell list.
Since you have a level of Cleric, all Cleric spells are on your class spell list, regardless of level. Any 5th level Cleric spell is on your class spell list.
2 The spell is of a level that you can normally cast.
Since your Druid can cast 5th level spells, this requirement is fulfilled. If you can cast 5th level spells, then a 5th level spell is of a level that you can normally cast. Done.
It's been suggested that you need to be able to cast a 5th level spell of the same class as the spell from the scroll. This isn't supported by the text of the rule, but let's imagine that's a requirement, just for the sake of argument. You can still cast the spell.
Since you can cast a 5th-level druid spell, you must have 5th level spell slots.
Since you are a 1st level cleric, you can cast Cure Wounds.
Note that, on page 201 of the Player's Handbook, it says
When a spellcaster casts a spell using a slot that is of a higher level than the spell, the spell assumes the higher level for that casting. For instance, if Umara casts magic missile using one of her 2nd-level spell slots, that magic missile is 2nd level.
Therefore, since you have a 5th level spell slot and can cast Cure Wounds, you can cast Cure Wounds at 5th level. This means you can cast a 5th level spell.
So no, you don't have to make the check.
Therefore, since any 5th-level cleric spell is on your class spell list, and is of a level you can normally cast, you do not need to make the check.
Just to be clear, this is not contradicted by the multiclassing rules.
On page 164 of the Player's Handbook, it says
If you have more than one spellcasting class, this table might give you spell slots of a level that is higher than the spells you know or can prepare. You can use those slots, but only to cast your lower-level spells.
One might misread this, as appears to have been done in another answer, to mean that you cannot use the higher slots to upcast your spells. However, that same section goes on to clarify, regarding a hypothetical multiclassed Ranger 4 / Wizard 3 character
... you have ... two 3rd-level slots. However you don't know any 3rd-level spells ... You can use the spell slots of those levels to cast the spells you do know -- and potentially enhance their effects.
So this character can clearly upcast the lower level spells they know with the higher level spell slots available due to multiclassing rules, even though neither of this character's classes are able to know spells of that higher level.
They are casting a spell of lower level, such as a 1st-level Cure Wounds spell, and then for that casting it becomes a higher level spell.
This means that a Level 8 Druid / Level 1 Cleric also would not need to make the check as they also have a level of cleric and a 5th-level spell slot, even though they haven't learned any spell with a minimum level of 5.
One additional note:
If upcasting a spell doesn't count as being able to normally cast a spell at that level, as some have suggested, then we get an absurd result. If a 9th level Wizard chooses not to learn any 5th level spells, then, by that logic, the Wizard wouldn't be able to cast a 5th level scroll. What about a 9th level cleric that just happens to prepare zero 5th level spells for the day? Do they lose the ability to use their 5th level scroll for the day, only to regain it the next day when they prepare a 5th level spell again?
It seems clear that this is not intended.