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Is the language given below regular or not ?

I feel it is regular.

The equivalent language is, L = {anblak ; n>=1,l>=1,k>=1 } - { a1b1a,  a1b1a,  a1b1a,  a1b2a,  a1b2a,  a1b3a1 and few more strings (but finite number of strings) }

We know that every finite language is a regular language and also set difference between any two regular languages is regular ... So can we say that the above language is regular ...

QUESTION TAKEN FROM PETER LINZ TEXTBOOK AND ANSWER WAS NOT GIVEN. So please verify whether i am correct ...???

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Best answer
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The equivalent language explanation correct.

Given language is = $a^*b^*a^* - \left \{ a^xb^ya^z \quad | \quad x+y+z \leq 5 \right \}$ which is rehular.
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Yes its regular.
 number of a,b,c can be (0,0,5) or (0,1,4) etc.There are definite possible combinations here.
After that any umber of a b c can be accepted
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aaaaaaa*b*a* + aaaaabb*a* + aaaabbb*a* + aaaabaa* + aaabbbb*a* + aaabbaa* + aaabaaa* +
+aabbbbb*a*+aabbbaa*+aabbaaa*+aabaaaa*+abbbbbb*a*+abbbbaa*+abbbaaa*+abbaaaa*+abaaaaa*+
bbbbbbb*a* + bbbbbaa* + bbbbaaa* + bbbaaaa* + bbaaaaa*+ baaaaaa*

is the regular expression for the grammar

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