Моєму дідусеві вже сімдесят років.

In Ukrainian, the present-tense verb to be is usually omitted in sentences like this.

So instead of saying something exactly like My grandfather is seventy years old, Ukrainian naturally says:

Моєму дідусеві вже сімдесят років.

Literally, it is closer to:

To my grandfather already seventy years.

This is the normal Ukrainian way to talk about age.

Because they are in the dative case.

Ukrainian usually expresses age with this pattern:

[person in dative] + [number] + років

So:

• мій → моєму = to my
• дідусь → дідусеві = to grandfather / to grandpa

Together, моєму дідусеві means to my grandfather, which is how Ukrainian structures age statements.

A very common model is:

• Мені двадцять років. = I am twenty years old.
• Йому сорок років. = He is forty years old.

Моєму is the dative singular masculine/neuter form of мій meaning my.

Since дідусеві is masculine singular and in the dative case, the possessive adjective has to match it:

• мій дідусь = my grandfather
• моєму дідусеві = to my grandfather

So the ending changes because of case agreement.

The base form is дідусь, which means grandfather or grandpa.

In this sentence it becomes дідусеві, the dative singular form.

So:

• дідусь = grandfather
• дідусеві = to grandfather / to grandpa

This is a very typical masculine noun change in Ukrainian when used in the dative.

Because numerals in Ukrainian affect the form of the noun that follows them.

With 5 and higher, Ukrainian normally uses the genitive plural.

So:

• 1 рік = 1 year
• 2 роки, 3 роки, 4 роки = 2, 3, 4 years
• 5 років, 10 років, 70 років = 5, 10, 70 years

That is why you get:

сімдесят років = seventy years

This number pattern is one of the most important things to learn in Ukrainian.

Вже usually means already.

In this sentence, it adds the idea of by now, already, or sometimes as much as:

Моєму дідусеві вже сімдесят років. = My grandfather is already seventy years old.

Without вже, the sentence would simply state the age:

Моєму дідусеві сімдесят років. = My grandfather is seventy years old.

So вже adds a nuance, not the basic meaning.

Yes. Дідусь is a very common and natural word for grandfather, often with a warm or affectionate tone, similar to grandpa in many contexts.

You may also see related words like:

• дід = grandfather / old man, depending on context
• дідусь = grandpa, grandfather

In many everyday family contexts, дідусь sounds very natural.

Yes, Ukrainian word order is fairly flexible.

The neutral order here is:

Моєму дідусеві вже сімдесят років.

But other orders are possible for emphasis, for example:

• Вже сімдесят років моєму дідусеві.
• Моєму дідусеві сімдесят років уже.

These can sound more emphatic, literary, or context-dependent.

For learners, the original order is the safest and most natural to use.

A helpful literal breakdown is:

• Моєму = to my
• дідусеві = grandfather / grandpa
• вже = already
• сімдесят = seventy
• років = years

So the sentence is literally:

To my grandpa already seventy years.

That literal structure helps explain why the dative case is used and why there is no word for is.

A useful stress guide is:

моє́му ді́дусеві вже сімдеся́т ро́ків

Approximate pronunciation for an English speaker:

mo-YE-mu DEE-du-se-vi vzhé sim-de-syAT RO-kiv

A few tips:

• є in моєму sounds roughly like ye
• ж in вже sounds like the s in measure
• и is not exactly English ee or ih; it is a separate Ukrainian vowel

If you want to sound natural, stress is very important in Ukrainian, so learning the stressed syllables helps a lot.